Solve Series Proof Homework: 0<b<1 Convergence & Limit

[CalTech>MIT]

Homework Statement

Let 0<b<1, show that \sum^{n}_{r=1} (1/r^b - \frac{n^1-b}{1-b}) converges as n goes to infinity and denote the limit by \beta = \beta(b).

Also, show that \sum^{infinity}_{n=1} \frac{(-1)^n-1}{n^b} + \beta(2^1-b - 1) = 0

Homework Equations

The Attempt at a Solution

Absolutely clueless!

**Sorry for the bad formatting, for I am new to PF.

 

[micromass]

Try an integral test...