Calc6.45

From Example Problems
Jump to: navigation, search

Discuss the convergence or divergence of the series \sum _{{n=1}}^{{\infty }}{\frac  {n!}{4^{n}}}.

Let us use the ratio test to see if this test converges or diverges.

\lim _{{n\rightarrow \infty }}\left|{\frac  {{\frac  {(n+1)!}{4^{{n+1}}}}}{{\frac  {n!}{4^{n}}}}}\right|=\lim _{{n\rightarrow \infty }}\left|{\frac  {n+1}{4}}\right|=\infty \,

Thus, by the ratio test, this series diverges.


Main Page : Calculus