Calc6.3

From Example Problems
Jump to: navigation, search

Discuss the convergence of \sum _{{n=1}}^{{\infty }}{\frac  {1}{n^{5}}}.

\int _{{1}}^{{\infty }}{\frac  {1}{x^{5}}}\,dx=-{\frac  {1}{4}}x^{{-4}}{\bigg |}_{{1}}^{{\infty }}=0+{\frac  {1}{4}}={\frac  {1}{4}}

This integral converges. Since the function is continuous, positive, and decreasing, by the integral test, this series converges.


Main Page : Calculus