Question Number 160259 by HongKing last updated on 26/Nov/21
$$\mathrm{Find}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\left(-\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}+\mathrm{1}} \:\frac{\mathrm{1}\centerdot\mathrm{4}\centerdot…\centerdot\left(\mathrm{3n}-\mathrm{2}\right)}{\mathrm{7}\centerdot\mathrm{9}\centerdot…\centerdot\left(\mathrm{2n}+\mathrm{5}\right)}\:=\:? \\ $$