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Question-211896




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

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