Question Number 148482 by mathdanisur last updated on 28/Jul/21
Commented by hknkrc46 last updated on 28/Jul/21
$$\bigstar\:\frac{\mathrm{1}}{\mathrm{78}}\:+\:\frac{\mathrm{2}}{\mathrm{79}}\:+\:\frac{\mathrm{3}}{\mathrm{80}}\:−\:\mathrm{3} \\ $$$$=\:\left(\frac{\mathrm{1}}{\mathrm{78}}\:−\:\mathrm{1}\right)\:+\:\left(\frac{\mathrm{2}}{\mathrm{79}}\:−\:\mathrm{1}\right)\:+\:\left(\frac{\mathrm{3}}{\mathrm{80}}\:−\:\mathrm{1}\right) \\ $$$$=\:\frac{−\mathrm{77}}{\mathrm{78}}\:+\:\frac{−\mathrm{77}}{\mathrm{79}}\:+\:\frac{−\mathrm{77}}{\mathrm{80}} \\ $$$$=\:−\mathrm{77}\left(\frac{\mathrm{1}}{\mathrm{78}}\:+\:\frac{\mathrm{1}}{\mathrm{79}}\:+\:\frac{\mathrm{1}}{\mathrm{80}}\right) \\ $$$$\bigstar\:\frac{−\mathrm{77}\left(\frac{\mathrm{1}}{\mathrm{78}}\:+\:\frac{\mathrm{1}}{\mathrm{79}}\:+\:\frac{\mathrm{1}}{\mathrm{80}}\right)}{\frac{\mathrm{1}}{\mathrm{78}}\:+\:\frac{\mathrm{1}}{\mathrm{79}}\:+\:\frac{\mathrm{1}}{\mathrm{80}}}\:=\:−\mathrm{77} \\ $$
Commented by mathdanisur last updated on 28/Jul/21
$${Thank}\:{you}\:{Ser} \\ $$