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...