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...
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...