Question Number 211896 by Spillover last updated on 23/Sep/24
Answered by BHOOPENDRA last updated on 23/Sep/24
$$=−\frac{\mathrm{1}}{\mathrm{2}}\left({Re}\underset{{z}=\mathrm{0}} {{s}}\left({f}\left({z}\right)\right)+{Res}\underset{{z}=−\mathrm{1}} {\:}\:\left({f}\left({z}\right)\right)\right) \\ $$$$=−\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{2}{n}−\frac{\mathrm{2}}{\mathrm{3}}\left(\mathrm{2}{n}^{\mathrm{2}} +\mathrm{1}\right)\right) \\ $$$$=\frac{\mathrm{2}{n}^{\mathrm{2}} −\mathrm{3}{n}+\mathrm{1}}{\mathrm{3}} \\ $$$$=\frac{\mathrm{2}{n}^{\mathrm{2}} −{n}−\mathrm{2}{n}+\mathrm{1}}{\mathrm{3}} \\ $$$$=\frac{\left(\mathrm{2}{n}−\mathrm{1}\right)\left({n}−\mathrm{1}\right)}{\mathrm{3}} \\ $$
Commented by Spillover last updated on 23/Sep/24
$${thanks}. \\ $$