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Question

Question: The sum to infinity of the given series \(\frac{1}{n} - \frac{1}{2n^{2}} + \frac{1}{3n^{3}} - \frac{...

The sum to infinity of the given series 1n12n2+13n314n4+....\frac{1}{n} - \frac{1}{2n^{2}} + \frac{1}{3n^{3}} - \frac{1}{4n^{4}} + .... is.

A

loge(n+1n)\log_{e}\left( \frac{n + 1}{n} \right)

B

loge(nn+1)\log_{e}\left( \frac{n}{n + 1} \right)

C

loge(n1n)\log_{e}\left( \frac{n - 1}{n} \right)

D

loge(nn1)\log_{e}\left( \frac{n}{n - 1} \right)

Answer

loge(n+1n)\log_{e}\left( \frac{n + 1}{n} \right)

Explanation

Solution

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9e9e.