{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 263 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 80 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 267 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 0 1 177 0 44 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1 " 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 4 4 0 0 0 0 0 0 -1 0 }{PSTYLE " Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "Tim Schorer Referat \+ 22.01.1998" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "Referat zum Thema endliche numerische Fol gen und Reihen" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 26 "Arithmetische Progression:" }} {EXCHG {PARA 0 "" 0 "" {TEXT 263 11 "Definition:" }{TEXT -1 63 "\nUnte r einer arithmetische Progression versteht man eine Folge " }{XPPEDIT 18 0 "f[1], f[2], bis f[n]" "6%&%\"fG6#\"\"\"&F$6#\"\"#*&%$bisG\"\"\"& F$6#%\"nGF," }{TEXT -1 92 " bei der jedes weitere Folgenglied aus dem \+ vorhergehenden Glied plus einem bestimmten Wert (" }{TEXT 265 1 "r" } {TEXT -1 32 ") berechnet wird. Wenn der Wert " }{TEXT 264 3 "r>0" } {TEXT -1 31 " ist, dann ist die Progression " }{TEXT 267 8 "wachsend" }{TEXT -1 8 ", falls " }{TEXT 266 3 "r<0" }{TEXT -1 7 ", dann " } {TEXT 268 7 "fallend" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "Zu Beginn, wie immer:" }{MPLTEXT 1 0 22 "\nrestart: with(plots) :" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 58 "Nun die allgemeine Form f \374r die arithmetische Progression:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "a[n]:=Anfangswert+(n-1)*r;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>& %\"fG6#%\"nG,&&%\"aGF&\"\"\"*&,&F'F+!\"\"F+F+%\"rGF+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "Anfangswert:=4;\n`***************`; \nfor i from 1 to 4 do\n f[i]:=Anfangswert+i*r;\nod;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,AnfangswertG\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%0***************G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"fG6# \"\"\",&\"\"%F'%\"rGF'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"fG6#\" \"#,&\"\"%\"\"\"%\"rGF'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"fG6#\" \"$,&\"\"%\"\"\"%\"rGF'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"fG6#\" \"%,&F'\"\"\"%\"rGF'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 93 "Der gesam te Wert der Folge:\n Bei diesem Folgenglied hat die Folge den folgen den Gesamtwert:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "Intervall:=4;\n Wert:=0: \nfor i from 1 to Intervall do\n f[i]:=Anfangswert+i*r;\n \+ Wert:=Wert+f[i];\nod: Wert;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*Int ervallG\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"#;\"\"\"%\"rG\"#5 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 25 "Geome trische Progression:" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 74 "Definition :\nUnter einer geometrischen Progression versteht man eine Folge " } {XPPEDIT 18 0 "f[1], f[2], bis f[n]" "6%&%\"fG6#\"\"\"&F$6#\"\"#*&%$bi sG\"\"\"&F$6#%\"nGF," }{TEXT -1 141 ", bei der jedes Glied aus dem vor hergehenden berechnet wird, imdem man das vorhergehende Glied mit eine r bestimmten Zahl multipliziert wird (" }{TEXT 269 1 "q" }{TEXT -1 2 " )." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "Beginn:" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 21 "restart: with(plots):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "Die allgemeine Form f\374r die geometrische Progression: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "a[n]=Anfangswert*q^(n-1);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/&%\"aG6#%\"nG*&%,AnfangswertG\"\"\")% \"qG,&F'F*!\"\"F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "Anfa ngswert:=4;\n`***************`;\nfor i from 2 to 6 do\n f[i]:=Anfang swert*q^(i-1);\nod;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,AnfangswertG \"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%0***************G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"fG6#\"\"#,$%\"qG\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"fG6#\"\"$,$*$%\"qG\"\"#\"\"%" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>&%\"fG6#\"\"%,$*$%\"qG\"\"$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"fG6#\"\"&,$*$%\"qG\"\"%F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"fG6#\"\"',$*$%\"qG\"\"&\"\"%" }}}{SECT 0 {PARA 4 " " 0 "" {TEXT -1 9 "Beispiel:" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Bei spiel:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "f[0]:=3; q:=2;\nf or i from 1 to 5 do\n f[i]:=f[i-1]*q^(i);\nod;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"fG6#\"\"!\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%\"qG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"fG6#\"\"\"\"\"'" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"fG6#\"\"#\"#C" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>&%\"fG6#\"\"$\"$#>" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>&%\"fG6#\"\"%\"%sI" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"fG6#\"\" &\"&/$)*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Der gesamte Wert der Folge:\n Bei " } {XPPEDIT 18 0 "f[i]" "&%\"fG6#%\"iG" }{TEXT -1 40 " hat die folge den \+ folgenden Gesamtwert:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "Wert:=0: \+ \nfor i from 1 to 3 do\n f[i]:=f[i-1]+i*r:\n Wert:=Wert+f[i];\nod: Wert;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&&%\"fG6#\"\"!\"\"$%\"rG\"# 5" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 9 "Beispiel:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 0 "" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{MARK "8 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }