Question Number 156900 by MathSh last updated on 16/Oct/21
$$\Omega_{\mathrm{1}} \:=\:\mathrm{1}\:-\:\frac{\pi}{\mathrm{2}}\:+\underset{\boldsymbol{\mathrm{n}}=\mathrm{2}} {\overset{\infty} {\sum}}\left(-\:\frac{\mathrm{1}}{\boldsymbol{\pi}}\right)^{\boldsymbol{\mathrm{n}}} \centerdot\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}} \\ $$$$\Omega_{\mathrm{2}} \:=\:\mathrm{1}\:-\:\frac{\pi}{\mathrm{2}}\:+\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{2}} {\overset{\infty} {\sum}}\left(-\:\frac{\mathrm{1}}{\boldsymbol{\mathrm{e}}}\right)^{\boldsymbol{\mathrm{n}}} \centerdot\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}} \\ $$$$\left.\mathrm{A}\left.\right)\left.\:\Omega_{\mathrm{1}} \:<\:\Omega_{\mathrm{2}} \:\:\:\mathrm{B}\right)\:\Omega_{\mathrm{1}} \:=\:\Omega_{\mathrm{2}} \:\:\:\mathrm{C}\right)\:\Omega_{\mathrm{1}} \:>\:\Omega_{\mathrm{2}} \\ $$