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Question Number 108688 by abdomsup last updated on 18/Aug/20

prove that   Σ_(n=−∞) ^∞  (1/((ax+1)^n ))  =−(π/a^n ) lim_(x→−(1/a))    (1/((n−1)!)){cotan(πx)}^((n−1))

$${prove}\:{that}\: \\ $$$$\sum_{{n}=−\infty} ^{\infty} \:\frac{\mathrm{1}}{\left({ax}+\mathrm{1}\right)^{{n}} } \\ $$$$=−\frac{\pi}{{a}^{{n}} }\:{lim}_{{x}\rightarrow−\frac{\mathrm{1}}{{a}}} \:\:\:\frac{\mathrm{1}}{\left({n}−\mathrm{1}\right)!}\left\{{cotan}\left(\pi{x}\right)\right\}^{\left({n}−\mathrm{1}\right)} \\ $$

Commented by mathdave last updated on 18/Aug/20

go ahead and prove dat

$${go}\:{ahead}\:{and}\:{prove}\:{dat} \\ $$

Commented by mathmax by abdo last updated on 18/Aug/20

this question is not for you sir...

$$\mathrm{this}\:\mathrm{question}\:\mathrm{is}\:\mathrm{not}\:\mathrm{for}\:\mathrm{you}\:\mathrm{sir}... \\ $$

Commented by mathdave last updated on 18/Aug/20

i thought he asking me to prove dat

$${i}\:{thought}\:{he}\:{asking}\:{me}\:{to}\:{prove}\:{dat}\: \\ $$$$ \\ $$

Commented by mathmax by abdo last updated on 18/Aug/20

no sir...

$$\mathrm{no}\:\mathrm{sir}... \\ $$

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