Recent content by greenteacup

Ohhh, okay, I think I understand now. So the coefficient would just be (-1)^{3}=-1?

Homework Statement The function f(x)=\frac{1}{1+x^{9}} can be expanded in a power series \sum^{\infty}_{0} a_{n}x^{n} with center c = 0. Find the coefficient a_{27} of x^{27} in this power series. 2. The attempt at a solution I can get to: \sum^{\infty}_{0} (-1)^{n}(-x^{9})^{n} which I...

Thank you so much, everyone! zcd, is the b_{n} you gave me less than \frac{1}{e^{n}} though? It seems like it should be bigger because the denominator is less...

Hmm. Could I make it \frac{e^{n}}{ne^{2n}}? Or \frac{ln(e^{n})}{ln(e^{2n})}?

Homework Statement \sum^{\infty}_{n=1} \frac{e^{n}+n}{e^{2n}-n^{2}} Homework Equations I have to use either the Comparison Test or the Limit Comparison Test to show whether the series converges or diverges. The Attempt at a Solution a_{n} = \frac{e^{n}+n}{e^{2n}-n^{2}} b_{n} =...

Homework Statement limit as x->\infty of arctan[(1/x)-1] 2. The attempt at a solution Well, my graphing calculator is showing a vertical asymptote at x=0 and a horizontal one at x=(what I think is) -\pi/4 I'm not really sure how to solve this though... hence me being here : / EDIT...