Question Number 140810 by mathsuji last updated on 12/May/21
$${Find}\:{the}\:{natural}\:{value}\:{of}\:\boldsymbol{{x}}\:{that} \\ $$$${satisfies}\:{the}\:{equation}: \\ $$$$\frac{\mathrm{1}}{\mathrm{6}\centerdot\mathrm{7}}\:+\:\frac{\mathrm{1}}{\mathrm{7}\centerdot\mathrm{8}}\:+\:\frac{\mathrm{1}}{\mathrm{8}\centerdot\mathrm{9}}\:+...+\:\frac{\mathrm{1}}{{x}\centerdot\left({x}+\mathrm{1}\right)}\:=\:\frac{\mathrm{1}}{\mathrm{12}} \\ $$