Question Number 32425 by naka3546 last updated on 24/Mar/18
$$\left(\:\frac{\mathrm{1}}{\mathrm{99}}\:−\:\mathrm{1}\right)^{\mathrm{108}} \:+\:\left(\frac{\mathrm{2}}{\mathrm{99}}\:−\:\mathrm{1}\right)^{\mathrm{107}} \:+\:\left(\frac{\mathrm{3}}{\mathrm{99}}\:−\:\mathrm{1}\right)^{\mathrm{106}} \:+\:…\:+\:\left(\frac{\mathrm{107}}{\mathrm{99}}\:−\:\mathrm{1}\right)^{\mathrm{2}} \:+\:\left(\frac{\mathrm{108}}{\mathrm{99}}\:−\:\mathrm{1}\right)\:\:=\:\:\:…. \\ $$