A8 - Math 128: Assignment 8 due Wednesday, Nov 23 by 4:30...

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Math 128: Assignment 8 due Wednesday, Nov 23 by 4:30 pm Koray Karabina (kkarabin@uwaterloo.ca) 1. Let a 1 = 3 and a n +1 = 15 + a n for n = 1 , 2 , 3 ,... . (a) Show that { a n } converges. Hint: Show that { a n } is positive, increasing, and bounded above by 5. (b) Find lim n →∞ a n . 2. Show that the series X n =1 1 n ( n + 2) converges and find its sum. Hint: Use partial fraction decomposition technique. 3. ( Geometric Series ) In parts (a)–(d), determine whether the series is convergent. If it is convergent, find its sum. (a) X n =1 ( - 5) n 8 2 n (b) X n =1 3 n + 4 n 5 n (c) X n =1 π n 3 n +1 (d) X n =1 3 n +1 e n - 1 4. ( Limit Divergence Test ) In parts (a)–(b), determine whether the series is convergent. (a) X n =1 1 + n 2 + 3 n (b) X n =1 2 n 2 + 3 n + 4 100 n 2 + 99 n - 98 5. ( Integral Test ) In parts (a)–(b), determine whether the series is convergent.
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