Lebl-Basic-Analysis-I · Problem 2.6.5

Sequences and Series

Mathematics · power-series-radius-convergence

Problem

For the following power series, find if they are convergent or not, and if so find their radius of convergence. a) ∑n=0∞2nxn\displaystyle\sum_{n=0}^{\infty} 2^n x^n b) ∑n=0∞nxn\displaystyle\sum_{n=0}^{\infty} n x^n c) ∑n=0∞n! xn\displaystyle\sum_{n=0}^{\infty} n! \, x^n d) ∑n=0∞1(2n)!(x−10)n\displaystyle\sum_{n=0}^{\infty} \frac{1}{(2n)!}(x-10)^n e) ∑n=0∞x2n\displaystyle\sum_{n=0}^{\infty} x^{2n} f) ∑n=0∞n! xn!\displaystyle\sum_{n=0}^{\infty} n! \, x^{n!}

Related theory

Browse the problem library