# Integral Test

1. Oct 8, 2012

### Bashyboy

1. The problem statement, all variables and given/known data
$\sum_{n=1}^{\infty} \frac{n^{k-1}}{n^k+c}$, where k is a positive integer.

2. Relevant equations

3. The attempt at a solution
I found that it was discontinuous at $x = (-c)^{1/k}$; and to determine if the sequence is decreasing, I took the

derivative which is--I think--$f'(x) = \frac{(k-1)x^{k-2}(x^k+c)-x^{k-1}(kx^{k-1}}{(x^k+c)^2}$
I am not quite sure how to simplify this, nor am I certain on how to find the intervals which the sequence is decreasing.

2. Oct 8, 2012

### Zondrina

Now that you've taken the derivative of f, ask yourself, what are the critical points? Those will allow you to find if f is decreasing as x → ∞.