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# How do I solve: Determine whether the series ((1+(2^k))/ ((3^k)-1))?

Determine whether the series ((1+(2^k))/ ((3^k)-1)) CONVERGES OR DIVERGES

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### 2 Answers

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- asimovLv 610 years agoFavorite Answer
k=1 , 3/2

k=2 , 5/8

k=3 , 10/26

the serie convergens to the asymptote 2^k/ 3^k = (2/3)^k

and for k-->oo , (2/3)^k =0

couse for every n , |n|<1 it will be convergens to 0

- MathPhDLv 610 years ago
These terms converge to 0, because the terms are positive and dominated by (9/4)(2/3)^k, which go to 0.

If you mean the sum of these terms, then the answer is still that it converges. This is because the sum with these dominating terms is a converging geometric series.

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