Find the sum of the series.

$\sum _{n=1}^{\mathrm{\infty}}\frac{2}{(n+8)(n+6)}$

Braxton Pugh
2020-11-24
Answered

Find the sum of the series.

$\sum _{n=1}^{\mathrm{\infty}}\frac{2}{(n+8)(n+6)}$

You can still ask an expert for help

aprovard

Answered 2020-11-25
Author has **94** answers

The series is:

$\sum _{n=1}^{\mathrm{\infty}}\frac{2}{(n+8)(n+6)}$

Simplify the series.

$\sum _{n=1}^{\mathrm{\infty}}\frac{2}{(n+8)(n+6)}=\sum _{n=1}^{\mathrm{\infty}}\frac{8-6}{(n+8)(n+6)}$

$=\sum _{n=1}^{\mathrm{\infty}}\frac{(n+8)-(n+6)}{(n+8)(n+6)}$

$=\sum _{n=1}^{\mathrm{\infty}}\frac{1}{(n+6)}-\frac{1}{(n+8)}$

Expand the summation.

$\sum _{n=1}^{\mathrm{\infty}}\frac{1}{(n+6)}-\frac{1}{(n+8)}=(\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}...)-(\frac{1}{9}+\frac{1}{10}+...)$

$=\frac{1}{7}+\frac{1}{8}$

$=\frac{15}{56}$

Simplify the series.

Expand the summation.

Jeffrey Jordon

Answered 2021-12-27
Author has **2313** answers

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