- #1
Bashyboy
- 1,421
- 5
Homework Statement
[itex]\sum_{n=1}^{\infty} \frac{n^{k-1}}{n^k+c}[/itex], where k is a positive integer.
Homework Equations
The Attempt at a Solution
I found that it was discontinuous at [itex]x = (-c)^{1/k}[/itex]; and to determine if the sequence is decreasing, I took the
derivative which is--I think--[itex]f'(x) = \frac{(k-1)x^{k-2}(x^k+c)-x^{k-1}(kx^{k-1}}{(x^k+c)^2}[/itex]
I am not quite sure how to simplify this, nor am I certain on how to find the intervals which the sequence is decreasing.