Chapter 9.3, Problem 51PE

a.

To determine

To perform the partial fraction decomposition.

To determine

To rewrite the infinite sum of $\frac{2}{1(3)}+\frac{2}{2(4)}+\frac{2}{3(5)}+\frac{2}{4(6)}+\frac{2}{5(7)}+\mathrm{........}$ using partial fraction decomposition of

  $\frac{2}{n(n+2)}$

To determine

To find the value of $\frac{1}{(n+2)}$ as $n\to \infty$

To determine

To find the sum from the part (b).