I have to determine whether the infinite sum (from n=1) of 1/n^(1+a) converges or diverges. Where 0 < a < 1
Comparison / Integral test
The Attempt at a Solution
I have tried using the ratio test but it gives me 1, so it cannot determine convergence or divergence.
I then tried using comparision test, comparing it to 1/n (which diverges) and 1/n^2 (which converges). But since 1/n^(1+a) is smaller than 1/n and greater than 1/n^2 I cannot make such comparison.
Then I used integral test where I let a=0.1 . This method tells me that for (a) greater than or equal to 0.1 the series converges. But how do I show that it converges (I think it converges) for (a) less than 0.1?