a) Find the interval of convergence for the series: $x - \frac{x^2}{2…

Previous year question for Engineering Mathematics-II.

Question

a) Find the interval of convergence for the series: $x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \dots$.

b) Prove that the series $\sum_{n=1}^\infty \frac{1}{n^p}$ is convergent when $p > 1$.

c) If the series $\sum_{n=1}^\infty a_n$ is convergent, show that $\lim_{n\to\infty} a_n = 0$.