Question Number 18640 by 99 last updated on 26/Jul/17
Commented by 99 last updated on 26/Jul/17
$${please}\:{solve}\:{question}\:{no}.\mathrm{6}\:.{please}... \\ $$
Answered by Tinkutara last updated on 28/Jul/17
$$\frac{\mathrm{1}}{\mathrm{1}×\mathrm{3}}\:+\:\frac{\mathrm{3}}{\mathrm{1}×\mathrm{3}×\mathrm{7}}\:+\:\frac{\mathrm{5}}{\mathrm{1}×\mathrm{3}×\mathrm{7}×\mathrm{11}}\:+\:... \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{1}}\:−\:\frac{\mathrm{1}}{\mathrm{3}}\right)\:+\:\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{1}×\mathrm{3}}\:−\:\frac{\mathrm{1}}{\mathrm{1}×\mathrm{3}×\mathrm{7}}\right) \\ $$$$+\:\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{1}×\mathrm{3}×\mathrm{7}}\:−\:\frac{\mathrm{1}}{\mathrm{1}×\mathrm{3}×\mathrm{7}×\mathrm{11}}\right)\:+\:... \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$
Commented by 99 last updated on 28/Jul/17
$${thanks}\:{sir} \\ $$