{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 " " -1 256 "" 0 1 0 0 0 0 0 1 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 "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 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 171 "Jan K\344stle \+ \+ \+ 24.11.97" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 256 22 "Vollst\344ndige I nduktion" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "Zu beweisen ist da\337 " } {XPPEDIT 18 0 "9^n-1" ",&)\"\"*%\"nG\"\"\"\"\"\"!\"\"" }{TEXT -1 21 " \+ durch 8 teilbar ist." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "Ann ahme:=9^n-1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(AnnahmeG,&)\"\"*%\" nG\"\"\"!\"\"F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "Induktionsanna hme:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "for n from 1 to 5 d o (9^n-1)/8 od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#\"* " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$?)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"%\"Q(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "n: ='n':" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "Induktionsschritt:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Schritt:=subs(n=n+1,Annahme) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(SchrittG,&)\"\"*,&%\"nG\"\"\"F *F*F*!\"\"F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Zusatz:=a*9 ^n;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'ZusatzG*&%\"aG\"\"\")\"\"*% \"nGF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "match(Schritt=Ann ahme+Zusatz,n,'S');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "S;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<#/%\"aG\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "assign(\");" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "Zusatz; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$)\"\"*%\"nG\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "15 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }