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# hw6sol - H om e w o r k 6 Sol u t ion P r o b l e m 1 Se c...

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Hom e work 6 Solution Probl e m 1 S ec tion 4 . 1 , Ex e r c i s e 4 , pag e 279 a) ͳ ൌ ቆ ͳሺͳ ൅ ͳሻ ʹ b) Both sides of P(1) shown in part (a) equal 1. c) ±ሺ ሻ ൌ ͳ ൅ ʹ ൅ ڮ ൅ ൌ ቆ ሺ ൅ ͳሻ ʹ d) For each, k 1 that P(k) implies P(k+1) ͳ ൅ ʹ ൅ ڮ ൅ ሺ ൅ ͳሻ ൌ ቆ ሺ ൅ ͳሻሺ ൅ ʹሻ ʹ e) ሺͳ ൅ ʹ ൅ ڮ ൅ ሻ ൅ ሺ ൅ ͳሻ ൌ ቆ ሺ ൅ ͳሻ ʹ ൅ ሺ ൅ ͳሻ ሺ ൅ ͳሻ Ͷ Ͷሺ ൅ ͳሻ Ͷ ሺ ൅ ͳሻ ൅ Ͷሺ ൅ ͳሻ Ͷ ൌൌ ሺ ൅ ͳሻ ൅ Ͷሺ ൅ ͳሻ൯ Ͷ ሺ ൅ ͳሻ ൅ Ͷ ൅ Ͷሻ Ͷ ሺ ൅ ͳሻ ሺ ൅ ʹሻ Ͷ ൌ ቆ ሺ ൅ ͳሻሺ ൅ ʹሻ ʹ ൌ ±ሺ ൅ ͳሻ f) We have completed both the basis step and inductive step so by the principle of mathematical induction the statement is true for every positive integer n.

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hw6sol - H om e w o r k 6 Sol u t ion P r o b l e m 1 Se c...

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