Question

Determine whether the series is convergent, absolutely convergent, conditionally convergent, or divergent.


On top of the summation sign (∑) is infinity. Under the summation sign is n=2, and right next to it (to the right of ∑ sign) is (n root of (n)-1)^n

(Sorry I don't know how to write the n root..(ex. cube root of etc..))

How would you do this problem?

I think I am stuck on the part with the square root..

Answer 1

nth root of x is x^1/n

nth root of (n-1)^n is n-1, is it not?

Answer 2

I think it is (n^(1/n)-1)^n

Using the ratio test,

T(n+1)/Tn
= ((n+1)^(1/(n+1))-1)^(n+1)/(n^(1/n)-1)^n

If you can show that that ratio is less than 1, you're home free.