Question Number 148838 by liberty last updated on 31/Jul/21
$$\:\frac{\mathrm{1}}{\mathrm{2}×\mathrm{3}×\mathrm{4}}\:+\frac{\mathrm{1}}{\mathrm{3}×\mathrm{4}×\mathrm{5}}+\frac{\mathrm{1}}{\mathrm{4}×\mathrm{5}×\mathrm{6}}+\frac{\mathrm{1}}{\mathrm{5}×\mathrm{6}×\mathrm{7}}+\frac{\mathrm{1}}{\mathrm{6}×\mathrm{7}×\mathrm{8}}+...+\frac{\mathrm{1}}{\mathrm{12}×\mathrm{13}×\mathrm{14}}=? \\ $$
Commented by JDamian last updated on 31/Jul/21
$${Can}\:{you}\:{confirm}\:{there}\:{is}\:{a}\:{missing}\:\frac{\mathrm{1}}{\mathrm{4}×\mathrm{5}×\mathrm{6}}? \\ $$
Commented by liberty last updated on 31/Jul/21
$$\mathrm{yes}\:\mathrm{typo} \\ $$
Commented by EDWIN88 last updated on 31/Jul/21
$$=\:\frac{\mathrm{22}}{\mathrm{273}}\:. \\ $$