# Math Help - Looking for Power Series

1. ## Looking for Power Series

Hey there, I know that

$\frac{t}{e^t-1} = \sum_{k=0}^\infty \frac{B_k}{k!} t^k$, where $B_k$ are the Bernoulli numbers. I am looking for a sequence $a_k$, such that $\frac{t}{e^t+e^{-t}} = \sum_{k=0}^\infty a_k t^k$.

Any ideas?

2. Originally Posted by EinStone
Hey there, I know that

$\frac{t}{e^t-1} = \sum_{k=0}^\infty \frac{B_k}{k!} t^k$, where $B_k$ are the Bernoulli numbers. I am looking for a sequence $a_k$, such that $\frac{t}{e^t+e^{-t}} = \sum_{k=0}^\infty a_k t^k$.

Any ideas?
What about $\frac{t}{e^t+e^{-t}}=\frac{e^tt}{e^{2t}+1}$ $=e^t\,\frac{t}{e^{2t}+1}$ and then you can multiply both series...?

Tonio

3. CAn you enlarge on that?