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For-what-value-of-p-does-the-series-n-1-e-n-2-e-2n-p-converge-




Question Number 210309 by Spillover last updated on 06/Aug/24
For what value of p does the series  Σ_(n=1) ^∞ (e^n /((2+e^(2n) )^p ))     converge
$${For}\:{what}\:{value}\:{of}\:{p}\:{does}\:{the}\:{series} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{e}^{{n}} }{\left(\mathrm{2}+{e}^{\mathrm{2}{n}} \right)^{{p}} }\:\:\:\:\:{converge} \\ $$
Commented by klipto last updated on 06/Aug/24
converge or diverge?
$$\boldsymbol{\mathrm{converge}}\:\boldsymbol{\mathrm{or}}\:\boldsymbol{\mathrm{diverge}}? \\ $$

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