Menu Close

Find-1-n-1-2-n-n-2n-2-n-1-x-5-n-3-n-1-n-ln-n-




Question Number 202473 by hardmath last updated on 27/Dec/23
Find:  1. Σ_(n=1) ^∞  ((2^n  ∙ n!)/((2n)!))          2. Σ_(n=1) ^∞  (((x + 5)^n )/(3^(n+1)  ∙ n ∙ ln(n)))
$$\mathrm{Find}: \\ $$$$\mathrm{1}.\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{2}^{\boldsymbol{\mathrm{n}}} \:\centerdot\:\mathrm{n}!}{\left(\mathrm{2n}\right)!}\:\:\:\:\:\:\:\:\:\:\mathrm{2}.\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\left(\mathrm{x}\:+\:\mathrm{5}\right)^{\boldsymbol{\mathrm{n}}} }{\mathrm{3}^{\boldsymbol{\mathrm{n}}+\mathrm{1}} \:\centerdot\:\mathrm{n}\:\centerdot\:\mathrm{ln}\left(\mathrm{n}\right)} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *