Calc6.50

From Example Problems
Jump to: navigation, search

Discuss the convergence or divergence of the series \sum _{{k=4}}^{{\infty }}\left({\frac  {1}{k}}-{\frac  {1}{k+2}}\right).

This is the sum of two telescopic series.

\sum _{{k=4}}^{{\infty }}\left({\frac  {1}{k}}-{\frac  {1}{k+2}}\right)=\sum _{{k=4}}^{{\infty }}\left({\frac  {1}{k}}-{\frac  {1}{k+1}}+{\frac  {1}{k+1}}-{\frac  {1}{k+2}}\right)={\frac  {1}{4}}+{\frac  {1}{5}}={\frac  {9}{20}}\,


Main Page : Calculus