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Does the following infinite series converge or diverge?


(1)/(2) - (2)/(9) + (4)/(27) + - (8)/(81) +
A. It Diverges; it does not have a sum

B. It converges; it does not have a sum

C. It Diverges; it has a sum

D. It converges; it has a sum

User Wu Li
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1 Answer

6 votes
The nth term is (presuming the denominator on the first is a typo)


-(n)/((-3)^n)

The ratio of successive terms is


( (n+1)/((-3)^(n+1)))/((n)/((-3)^n)) = (n+1)/(-3n)

The limit is -1/3, absolute value less than 1, so the series converges. It has a sum -- that's what converges means.

User Jaseem Abbas
by
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