Hello,

So, I have this problem that is wanting me to find two particular p-series that satisfy some particular conditions. I don't really know how to approach this problem and I'm not sure I even understand what is being asked.

The problem:

"Find two p-series: $\displaystyle \sum_{k=1}^{\infty}c_k$ and $\displaystyle \sum_{k=1}^{\infty}d_k$ such that $\displaystyle \sum_{k=1}^{\infty}\frac{8(-1)^kk-7(k)^\frac{1}{2}}{k^\frac{3}{2}} = \sum_{k=1}^{\infty}((-1)^kc_k + d_k)$.

Your answer should be the formulas for $\displaystyle c_k$ and $\displaystyle d_k$ separated by commas.Both terms should be of the form $\displaystyle \frac{c}{k^p}$ for some constants $\displaystyle c$ and $\displaystyle p$. Note that $\displaystyle c_k$ should be first."

If anyone has any hints as to how to approach this (for example, is there a simple matter of algebraic finagling to be done or some other "hidden" method?), I would be grateful.

Thanks