Prove Series Convergent: SUM (-1)^n * (1/n)^1+(1/n)

[PlantPage55]

Hey everyone,
This one should be a little bit easier. I'm supposed to prove that this series is convergent - but when I applying the ratio test I can't find a ratio that fits the rules.

SUM (-1)^n * (1/n)^1+(1/n)

Thanks again!

 

[tkhunny]

I don't understand what you have written. Can you format better?

 

[Razor X]

I’m assuming you mean:

Sum of [(-1)^n][(1/n)^[1 + (1/n)]] from n=1 to infinity

Apply the alternating series test:

| [(-1)^n][(1/n)^[1 + (1/n)]] | -> 0 as n -> infinity

and

| [(-1)^(n +1)][(1/(n+1))^[1 + (1/(n+1))]] | < | [(-1)^n][(1/n)^[1 + (1/n)]] |

therefore the series converges by the alternating series test.

Sorry about the lack of symbolic notation...i still need to get myself using TeX.

 

[PlantPage55]

ah ha! Thank you very much!