# hw92 - 9.2 Pages 461-463 1-29 odd 1 1 is a geometric series...

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9.2 Pages 461-463 # 1-29 odd 1. 1 1 7 k k =    is a geometric series with 1/7 ar == . So 11 1 77 16 6 1 S = . 7. 2 1 1 –– ; 1 21 32 43 k kk = =+++ 1 1 1 1 1 –1 23 2 1 2 1 n S nn n n =+ + + + 1 1; n = + 1 lim lim –1 –1, n S n →∞ →∞ = so 2 –1 k = = 9. 1 !1 2 6 100 10,000 1,000,000 100 k k k = = ++ + Consider {} , n a where , . 100 100 n aa a + + 0 n a > for all n, and for n >99, 1 , + > so the sequence is eventually an increasing sequence, hence lim 0. n n a →∞ The sequence can also be described by ! , 100 n n n a = hence 1 ! 100 k k k = diverges. We will revisit this sequence with a different method in section 9.4. 3. 0 00 45 k = ∞∞    +       ∑∑ 0 1 4 k k = is a geometric series with 1, 1 / 4 . So 4 13 3 1 44 S = . 0 1 5 k k = is a geometric series with 1 / 5 . So 5 6 1 55 S = .

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hw92 - 9.2 Pages 461-463 1-29 odd 1 1 is a geometric series...

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