Calc6.69

From Example Problems
Jump to: navigation, search

Discuss the convergence or divergence of the series \sum _{{n=1}}^{{\infty }}\left({\frac  {2n}{100}}\right)^{n}.

Using the root test, we have

\lim _{{n\rightarrow \infty }}{\sqrt[ {n}]{\left({\frac  {2n}{100}}\right)^{n}}}=\lim _{{n\rightarrow \infty }}{\frac  {2n}{100}}=\infty

Thus, since the limit goes to infinity, the series diverges by the root test.


Main Page : Calculus