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simlify-the-sum-S-k-0-n-1-x-e-i2kpi-x-e-i2kpi-




Question Number 28363 by abdo imad last updated on 24/Jan/18
simlify the sum   S= Σ_(k=0) ^(n−1)   ((x+ e^(i2kπ) )/(x −e^(i2kπ) ))  .
$${simlify}\:{the}\:{sum}\:\:\:{S}=\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:\frac{{x}+\:{e}^{{i}\mathrm{2}{k}\pi} }{{x}\:−{e}^{{i}\mathrm{2}{k}\pi} }\:\:. \\ $$
Answered by ajfour last updated on 24/Jan/18
S=((n(x+1))/(x−1)) .
$${S}=\frac{{n}\left({x}+\mathrm{1}\right)}{{x}−\mathrm{1}}\:. \\ $$

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