# Questions tagged [calculus]

For basic questions about limits, continuity, derivatives, integrals, and their applications, mainly of one-variable functions. For questions about convergence of sequences and series, this tag can be use with more specialized tags.

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### Finding values that make a series convergent

So I was given the following prompt: When $x=−2$, for what values of p does the series converge? $$\sum_{n=1}^\infty\left(\frac{(-1)^{n+1}(x-3)^n}{5^n\cdot n^p}\right)$$ I ended up working out this ...
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### Taylor Series, find the sum of a given convergent series

By recognizing the series $$-(\frac{1}{2})-\frac{(\frac{1}{2})^2}{2}-\frac{(\frac{1}{2})^3}{3}-⋯\frac{(\frac{1}{2})^n}{n}-⋯$$ as a Taylor Series evaluated at a particular value of x, find the sum of ...
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