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Z 0 v}0DWingdings. Z 0 v}0@ . @n?" dd@  @@`` 4,<{   ?Db$i,0t&(PR$V;,0V \PR$NaRA G F2$4yS 2$62(ׯ;2$!VӼ>ɇR;r2$-GldM*y2$Sh.ܷC> 2$g>m%uQA.u"2$n_{ϷY *y$2$UM iEU &2$ͪ#&$g𘥴J (2$%HϾ<-W-hY*2$byzF&'' ],2$-<,B8A=.2$6q5nq/2$>%>錕juDn12$hhh{~0[32$: ml}E_W5 0AA@3ʚ;ʚ;g4GdGd$v}0ppp@ <4ddddPa0. 80___PPT10 ppHModern akola CZ.1.07/1.5.00/34.0827$%HMatematika 5.4  Posloupnosti a Yady%%Autor:PaedDr. JiY Kocman Nzev: 5.4.5 U~it matematick indukceAA\Datum vytvoYen: 4.3. 2013 Clov skupina: }k gymnzia Vzdlvac oblast, vzdlvac obor: Matematika Anotace: Materil je ur en pro procvi ovn dovednost a znalost z pYedchozho materilu. PYnosem je aplikovn zskanch dovednost krom zkladnch loh i v lohch z geometrie a kombinatoriky.LpPPg    /8    \ T @ <(  < < <`wW  DCvi en 4  < <"`Zq` *Doka~te, ~e pro sou et vnitYnch hlo konvexnho n  helnku plat vztah: Sn = 180( n - 2).0_M L^R < 6G 2XR  < 02 dR  < <MGt;  < <Y"`z  JPo et vrcholo  < <t "`z} FSou et hlo 8  < <t z #\ x 3 180 4 360 3 540 atd& ==4 < <^ p  > Dokaz: < 0' "`   *Pro n = 3 plat  sou et hlo trojhelnku je 180=180( 3  2). PYedp.: pro k lib. je SZZ>AH < 0޽h ? 3380___PPT10.#r_ f ;Z (   "Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0`/ 0DArialngs. Z 0 v}0"DWingdings. Z 0 v}0@ . @n?" dd@  @@`` 4,<{   ?Db$i,0t&(PR$V;,0V \PR$NaRA G F2$4yS 2$62(ׯ;2$!VӼ>ɇR;r2$-GldM*y2$Sh.ܷC> 2$g>m%uQA.u"2$n_{ϷY *y$2$UM iEU &2$ͪ#&$g𘥴J (2$%HϾ<-W-hY*2$byzF&'' ],2$-<,B8A=.2$6q5nq/2$>%>錕juDn12$hhh{~0[32$: ml}E_W5 0AA@3ʚ;ʚ;g4GdGd$v}0ppp@ <4ddddPa0. 80___PPT10 ppHModern akola CZ.1.07/1.5.00/34.0827$%HMatematika 5.4  Posloupnosti a Yady%%Autor:PaedDr. JiY Kocman Nzev: 5.4.5 U~it matematick indukceAA\Datum vytvoYen: 4.3. 2013 Clov skupina: }k gymnzia Vzdlvac oblast, vzdlvac obor: Matematika Anotace: Materil je ur en pro procvi ovn dovednost a znalost z pYedchozho materilu. PYnosem je aplikovn zskanch dovednost krom zkladnch loh i v lohch z geometrie a kombinatoriky.LpPPg    /8  f    @ <f (  < < <`wW  DCvi en 4  < <"`Zq` *Doka~te, ~e pro sou et vnitYnch hlo konvexnho n  helnku plat vztah: Sn = 180( n - 2).0_M L^R < 6G 2XR  < 02 dR  < <MGt;  < <Y"`z  JPo et vrcholo  < <t "`z} FSou et hlo 8  < <t z #\ x 3 180 4 360 3 540 atd& ==4 < <^ p  > Dokaz: < 0' "`    Pro n = 3 plat  sou et hlo trojhelnku je 180=180( 3  2). PYedp.: pro k lib. je Sk = 180( k  2) a dok. Sk+1 = 180( k  1).JY  ,A&H < 0޽h ? 3380___PPT10.#r  r  (   "Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0`/ 0DArialngs. Z 0 v}0"DWingdings. Z 0 v}0@ . @n?" dd@  @@`` 4,<{   ?Db$i,0t&(PR$V;,0V \PR$NaRA G F2$4yS 2$62(ׯ;2$!VӼ>ɇR;r2$-GldM*y2$Sh.ܷC> 2$g>m%uQA.u"2$n_{ϷY *y$2$UM iEU &2$ͪ#&$g𘥴J (2$%HϾ<-W-hY*2$byzF&'' ],2$-<,B8A=.2$6q5nq/2$>%>錕juDn12$hhh{~0[32$: ml}E_W5 0AA@3ʚ;ʚ;g4GdGd$v}0ppp@ <4ddddPa0. 80___PPT10 ppHModern akola CZ.1.07/1.5.00/34.0827$%HMatematika 5.4  Posloupnosti a Yady%%Autor:PaedDr. JiY Kocman Nzev: 5.4.5 U~it matematick indukceAA\Datum vytvoYen: 4.3. 2013 Clov skupina: }k gymnzia Vzdlvac oblast, vzdlvac obor: Matematika Anotace: Materil je ur en pro procvi ovn dovednost a znalost z pYedchozho materilu. PYnosem je aplikovn zskanch dovednost krom zkladnch loh i v lohch z geometrie a kombinatoriky.LpPPg    /8      @ < (  < < <`wW  DCvi en 4  < <"`Zq` *Doka~te, ~e pro sou et vnitYnch hlo konvexnho n  helnku plat vztah: Sn = 180( n - 2).0_M L^R < 6G 2XR  < 02 dR  < <MGt;  < <Y"`z  JPo et vrcholo  < <t "`z} FSou et hlo 8  < <t z #\ x 3 180 4 360 3 540 atd& ==4 < <^  z d  > Dokaz:2 < 0' "` \ Pro n = 3 plat  sou et hlo trojhelnku je 180=180( 3  2). PYedp.: pro k lib. je Sk = 180( k  2) a dok. Sk+1 = 180( k  1). Sk+1 = Sk + 180 ( dala trojhelnk) = 180( k  2) + 180 = 180(k  2 + 1) = 180( k  1). Zvr: loha je dokzna~Y    vAH < 0޽h ? 3380___PPT10.#rG N # (   "Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0`/ 0DArialngs. Z 0 v}0"DWingdings. 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Z 0 v}0"DWingdings. Z 0 v}0@ . @n?" dd@  @@`` @   ob$i,0t&(PR$V;,0V \PR$NaRA G F2$4yS 2$62(ׯ;2$!VӼ>ɇR;r2$-GldM*y2$Sh.ܷC> 2$g>m%uQA.u"2$n_{ϷY *y$2$UM iEU &2$ͪ#&$g𘥴J (2$%HϾ<-W-hY*2$byzF&'' ],2$-<,B8A=.2$6q5nq/2$>%>錕juDn12$hhh{~0[32$: ml}E_W52$Eh=hw BZ62$ZH@(V~BOg.92$rk4.) < 0AA@3ʚ;ʚ;g4BdBd$v}0(ppp@ <4ddddPa0. 80___PPT10 ppHModern akola CZ.1.07/1.5.00/34.0827$%HMatematika 5.4  Posloupnosti a Yady%%Autor:PaedDr. JiY Kocman Nzev: 5.4.5 U~it matematick indukceAA\Datum vytvoYen: 4.3. 2013 Clov skupina: }k gymnzia Vzdlvac oblast, vzdlvac obor: Matematika Anotace: Materil je ur en pro procvi ovn dovednost a znalost z pYedchozho materilu. 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 ^  0 6 0 S A  ??"?08  $D 0.  0 0tR_ "`/q9O,$ 0 Z PYedpoklad: Pro libovoln k pYirozen plat:..^  0 6  0 S A  ??"?I8  $D 0  0 <|U_ "`"qB,$ 0 = Dokazujeme: ^ 0 6 0 S A  ??"? 8  $D 0^ 0 6(( 0 S A ??"?8 $D 0^ 0 6(( 0 S A ??"?%  8 $D 0 0 <\_ "` q ,$  0 8Plat:^ 0 6 0 S A ??"? k 8 $@  0 0 <^_ "`  ,$  0 9a vraz^ 0 611 0 S A ??"?  8 $@  0 0 <d_ "` T  ,$  0 V$je dliteln tYemi 0 <@i_ "` M  ,$ 0 > Zvr: 0 0k_ "`Iqi,$ 0 HDan vztah je dokzn.H 0 0޽h ? 33==___PPT10i=.#00+D;' = @B Dp;' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*0DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 0%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* 0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* 0D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* 0%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* 0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* 0DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 0%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* 0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* 0D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*0Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*0Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*0D' =%(DU' =%(D' =A@      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmropqstuvwxyz{|}~BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*0D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*0D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*0D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*0D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*0D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*0D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*0D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*0D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*0D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*0D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*0D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*0D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*0D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*0++0+ 0~  ++0+ 0  ++0+0  ++0+0  ++0+0  ++0+0~  ++0+0~  +D    4 (  4 4 <_ wW  DCvi en 3  4 <_ "`Zq` Na kolik st dl rovinu n pYmek, kter prochzej jednm bodem. Vyslovte hypotzu a doka~te ji indukc.llB 4 c $D/::c ,$@ 0B 4 c $D2z 2,$D 0B 4 c $D jS ,$D 0B  4 c $D  ,$D  0 4 <Ĺ_ "`# ,$ 0 HPo et pYmek  4 <_ "`,$ 0 FPo et sti h 4 <T_ y T1 ,$D 0 t 1 2 2 4 3 6 4 8 atd& ;;2 4 <_ F M  f ,$  0 :Hypotza 8 4 <_ f b,$ 0 fN pYmek s danou vlastnost dl rovinu na 2n st44H 4 0޽h ? 3399___PPT109.# +c%Dx8' = @B D38' = @BA?%,( < +O%,( < +D ' =%(D ' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*4D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*4D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*4D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*4D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*4D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*4Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4 %(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*4 D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*4 Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*4D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*4Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4 %(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*4 D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*4 Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*4D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*4Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4!%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*4!D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*4!Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* 4%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* 4D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* 4D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4!,%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*4!,D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*4!,D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4,;%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*4,;D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*4,;DN' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*4D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*4D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*4D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*4++0+4  ++0+4  ++0+4~  ++0+4~  +d pDd(  D^ D 6d D C A &?"?] f &^ D 6%%j D S A )??"?t ~ )^  D 6d D C A *?"?z *^  D 6d  D C A +?"?"Y +^  D 6d  D C A ,?"?U  ,j D S A /??"?F   / D <dV f t ~LBylo u~ito vztaho pro kombina n sla''^ D 6j D C A 0?#" `?Z 0^ D 6j D C A 1?#" `?~  1H D 0޽h ? 3380___PPT10.#pyxVM/A~f]MS84\ƅ*q@/(Ѥ +II"~@$'$ٝZ!}7ۙymnO/zT ZlsL.qEukZoO'/_^S?SD d鹎g+;//scʤOe[=eXi*8k\VI%d=y/S"OJ>S_5P_ynֽK,@x&ifad4rCzn#*Fd1FGbq5XCAlOcz&AOg2S^$b?`2(K[A!ں̊kK01nF~\F\"1UQ=V//Mڜ^ $u4u,іgד^u>tF5r}7 Uko5P{5NθK&/[RdxVM/A~f$JġB$M7=9p$%%GMH ?_?W]vUmG*}7ۙsfywooZN; F>q^ukZBgTa)eDIz` "o΋~1nG춾k=z1WQN;Tpf_[6XhKX:f0_q~?=Pm~awv?N|% yynֽJ]=II#uֆyF'&wryXbv%gt6IH(fR ODck,mH+fO}'w <=`Lf"72T̿=C{=$d4rA\aeqӋEU)XJ9iRSbЛ84QOPI{`\\u 힝O.\ z 5*ݨ8VL\{1>IbKĬG \eTxVMK@}iFA-x(xQɃz TгV,ԏj{S G/O8lb S ۙ7Ns];} cPPc t\뺮[z dAyrNM摧_1$&JV(rcʤkϯL=n9a!M'Tp|~Xؠ(VYZ!W}nV4>=F-{3٥V>S% ۩b6  jrC;A|O#gFD5<>~}*#mhQGsbæ6yUe Q,\NW.plVtD$T^dq۱jBGj1TAzּbcjIu,uю'.>\5QS j"}d:j>M|+^j xVJBAfFiD MH*ٔA 4,Z-Z*"j׮ZP/mvf m"?9x|g3x 30P1{e1%>u4M6;S$qwW@1d {Q!kw^^R[筶Pgz,#rZgzRؤ}$n;RDMN z6T:$'E^W^\[q9?@Ȼm˂xLG0S-ܜ_LmsB8/ \6<C/Qs5֋8>&EkfW~;_HNC{3Bz Gca)q"G(%(0y^?4QD:c\)_Fr*^'X%<=(Ht;sB]bθ;wź͚E v-{/ )ܒzaZX_??3  ^ jlkpE3c92 &?G|mfY,H9ks6я[͵@/ @+{Vnrt\T\\dLt%y՟og_@ǘL y?+[>OߎsKʄ 4h&lwd3OAS ?ų7$y?4 d_.hm6# ʁr@9 &2An?Ѿ،M?:(13`eX?bԬN;w"z.$g%cA}yL,I`=59~ rۻ̵^={* o1$ 5=kH)_YvLvutrO>+7Z#ƞX4$òxak|$?0/wz4E>sZhNOzgg֪ڊ>ͻ;3̻n;>m0PQc4\ ma?'à~9*~3H/bH};RPag^~ŝs{|;u jr]SŊ80{=~kbR!5P/Ox'( @"W] j*_-YYU?AZu}lV\.Y1}Ô6GɅF:2l2GH;~<eY|&(/NLkVGay3&!jRK1E#[+c. hh0Cy="ME鹬rs|Ss苽!z!Mĩ';0z[rޞ[O>Us0ߨ]StiK,/; )#1z\%rD*E33iJ xp^RЀ3ÿ lHbP  LPÄ!1 4Yv(bW< ]P^b <*1@ݐq|R> d;0TD\ L!V~gs Hb"~!2'bOzC? rB x{V;s@Gā>*Ef1#00sAzeEi% %y z <@)`73|T"C{1(5aS-T`(0g$022%sq12@ VFFF&C9H2u2MbM`~lNd`g`+`jf`9K9 &n!>32Ԥ8̆0ە!XgK<`=U*+C9=TV0TF4 ~jl?RLO-T m H1S&R Ihf!rfƮgjxp^RЀ3ÿ lHbP  LPÄ!1 4Yv(bW< ]P^b <*1@ݐ^/I#3+SrRIp101"X}" 0e(#!d@> f 4Kȱd/ +A Yr@"Z`a8eƌI[y[f&秕(&d)0\b @>grS! 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Z 0 v}0DWingdings. Z 0 v}0@ . @n?" dd@  @@`` H   ob$i,0t&(PR$V;,0V \PR$NaRA G F2$4yS 2$62(ׯ;2$!VӼ>ɇR;r2$-GldM*y2$Sh.ܷC> 2$g>m%uQA.u"2$n_{ϷY *y$2$UM iEU &2$ͪ#&$g𘥴J (2$%HϾ<-W-hY*2$byzF&'' ],2$-<,B8A=.2$6q5nq/2$>%>錕juDn12$hhh{~0[32$: ml}E_W52$Eh=hw BZ62$ZH@(V~BOg.92$rk4.) < 0AA@3ʚ;ʚ;g4GdGd$v}0ppp@ <4ddddPa0. 80___PPT10 pp?  %HModern akola CZ.1.07/1.5.00/34.0827$%HMatematika 5.4  Posloupnosti a Yady%%Autor:PaedDr. JiY Kocman Nzev: 5.4.5 U~it matematick indukceAA\Datum vytvoYen: 8.3. 2013 Clov skupina: }k gymnzia Vzdlvac oblast, vzdlvac obor: Matematika Anotace: Materil je ur en pro procvi ovn dovednost a znalost z pYedchozho materilu. PYnosem je aplikovn zskanch dovednost krom zkladnch loh i v lohch z geometrie a kombinatoriky.LpPPg    $ . /8  S jbH(  H H <`/1=p  TPOU}IT ZDROJE: H <71NH@8___PPT9 doc. RNDr. ODVRKO, O., DrSc.: Matematika pro gymnzia  posloupnosti a Yady, 1. vydn Praha Prometheus, spol. s r. o. 1995. 126 s. ISBN 80-85849-91-7 PETKOV, J. , MATEMATIKA  pYprava k maturit a pYijmacm zkouakm na vysok akoly, 1. vydn Praha Prometheus, spol. s r. o. 1998, 303 s. ISBN 80-7196-099-3BB,c  08X H \A޽h ?Balic papr"` 33___PPT10i.-@+D=' = @B +r.V . G(   MRovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0`/ 0DArialngs. Z 0 v}0DWingdings. 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