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Question-18640




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

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