frac{1}{{1!(n - 1),!}} + frac{1}{{3!(n - 3)!} | vedclass

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Question

(b) Multiplying each term by $n!$ the question reduces to $\frac{{n!}}{{1!(n - 1)!}} + \frac{1}{{3!}}.\frac{{n!}}{{(n - 3)\,!}} + \frac{1}{{5!}}.\frac

Vedclass · Accepted Answer

$\frac{{{2^{n - 1}}}}{{n!}}$; $n$ ની દરેક કિમત માટે

Vedclass · Answer

(b) Multiplying each term by $n!$ the question reduces to $\frac{{n!}}{{1!(n - 1)!}} + \frac{1}{{3!}}.\frac{{n!}}{{(n - 3)\,!}} + \frac{1}{{5!}}.\frac{{n!}}{{(n - 5)!}} + ....$

$ = {\,^n}{C_1} + {\,^n}{C_3} + {\,^n}{C_5} + .... = {2^{n - 1}}$.

Thus $\frac{1}{{1!(n - 1)!}} + \frac{1}{{3!(n - 3)!}} + \frac{1}{{5!(n - 5)!}} + ....$

$ = \frac{1}{{n!}}{2^{n - 1}}$.

$\frac{1}{{1!(n - 1)\,!}} + \frac{1}{{3!(n - 3)!}} + \frac{1}{{5!(n - 5)!}} + .... = $

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