Question

how do you if this series converges or diverges.

Answer 1

\[\sum_{n=1}^{\infty} n/(n+1)2^n\]

Answer 2

there are many test which you can perform
1) Divergence Test
2) Integral Test
3) Ratio Test
4) Limit Comparison Test
others which I don't remember

Answer 3

no 2^n is also in the denominator

Answer 4

\[\sum _{n=1}^{\infty } \frac{n}{(n+1)2^n}\]
1) Divergence Test is inconclusive
2)By ratio test \[\frac{n+1}{(n+2)2^{n+1}}*\frac{(n+1)2^n}{n}\]
\[\frac{2^n}{2^{n+1}}\frac{(n+1)^2}{n(n+2)}\]
we get 1/2 which is less than 1 , so series converge by ratio test

Answer 5

Let me know, if you need more clarification above

Answer 6

i understand! thank you!