Please help me out here.
The problem:
Given real numbers $X$ and $\epsilon$, with $X\neq 0$ and $\epsilon > 0$, calculate the sum of the series with the accuracy $\epsilon$ (for $\epsilon = 10^{-3}, 10^{-4}, 10^{-5}, 10^{-6}$) and specify the number of summands. Put results into columns $\epsilon$, sum, $N$. Run the calculation only for the first 10 terms.
$\sum_{k=0}^\infty\frac{(-1)^k}{((k+1)!)^2}\bigg(\frac{x}{2}\bigg)^{2(k+1)}$
This actually is a problem for my programming class, but I can't understand math behind the problem. What is X here? How can I perform these calculations with the given accuracy. Pls. advice if possible. Thanks!!