Answer to Question #272249 in Real Analysis for Sourav

Question

Show that the series 8/(n⁴+x⁴) is uniformly convergent for all real values of x. n=1 to infinity .

Answer 1

since $|\frac{8}{n^4+x^4}|\le \frac{8}{n^4}$ and series $\sum \frac{8}{n^4}$ converges, then series $\sum \frac{8}{n^4+x^4}$ converges as well