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Question Number 148482 by mathdanisur last updated on 28/Jul/21

Commented by hknkrc46 last updated on 28/Jul/21

★ (1/(78)) + (2/(79)) + (3/(80)) − 3 = ((1/(78)) − 1) + ((2/(79)) − 1) + ((3/(80)) − 1) = ((−77)/(78)) + ((−77)/(79)) + ((−77)/(80)) = −77((1/(78)) + (1/(79)) + (1/(80))) ★ ((−77((1/(78)) + (1/(79)) + (1/(80))))/((1/(78)) + (1/(79)) + (1/(80)))) = −77

$$\bigstar\:\frac{\mathrm{1}}{\mathrm{78}}\:+\:\frac{\mathrm{2}}{\mathrm{79}}\:+\:\frac{\mathrm{3}}{\mathrm{80}}\:−\:\mathrm{3} \\ $$$$=\:\left(\frac{\mathrm{1}}{\mathrm{78}}\:−\:\mathrm{1}\right)\:+\:\left(\frac{\mathrm{2}}{\mathrm{79}}\:−\:\mathrm{1}\right)\:+\:\left(\frac{\mathrm{3}}{\mathrm{80}}\:−\:\mathrm{1}\right) \\ $$$$=\:\frac{−\mathrm{77}}{\mathrm{78}}\:+\:\frac{−\mathrm{77}}{\mathrm{79}}\:+\:\frac{−\mathrm{77}}{\mathrm{80}} \\ $$$$=\:−\mathrm{77}\left(\frac{\mathrm{1}}{\mathrm{78}}\:+\:\frac{\mathrm{1}}{\mathrm{79}}\:+\:\frac{\mathrm{1}}{\mathrm{80}}\right) \\ $$$$\bigstar\:\frac{−\mathrm{77}\left(\frac{\mathrm{1}}{\mathrm{78}}\:+\:\frac{\mathrm{1}}{\mathrm{79}}\:+\:\frac{\mathrm{1}}{\mathrm{80}}\right)}{\frac{\mathrm{1}}{\mathrm{78}}\:+\:\frac{\mathrm{1}}{\mathrm{79}}\:+\:\frac{\mathrm{1}}{\mathrm{80}}}\:=\:−\mathrm{77} \\ $$

Commented by mathdanisur last updated on 28/Jul/21

Thank you Ser

$${Thank}\:{you}\:{Ser} \\ $$

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