Answer to Question #275064 in Real Analysis for Rampus

Question #275064

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




1
Expert's answer
2021-12-07T09:09:30-0500

since 8n4+x48n4|\frac{8}{n^4+x^4}|\le \frac{8}{n^4} and series 8n4\sum \frac{8}{n^4} converges, then series 8n4+x4\sum \frac{8}{n^4+x^4} converges as well


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