if a_1 , a_2 , a_3 , a_4 are the coefficient of any four four consecutive terms in the expansion of (1+x)^n then (a_1 /(a_2 +a_1 ))+(a_3 /(a_3 +a


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Question Number 63858 by gunawan last updated on 10/Jul/19

$if a_{1}, a_{2}, a_{3}, a_{4} are the coefficient$ $of any four four consecutive$ $terms in the expansion of {(1 + x)}^{n}$ $then \frac{a_{1}}{a_{2} + a_{1}} + \frac{a_{3}}{a_{3} + a_{4}} is equal to . . .$
	Answered by ajfour last updated on 10/Jul/19

	$v = \frac{^{n} C_{r - 1}}{^{n} C_{r} +^{n} C_{r - 1}} + \frac{^{n} C_{r + 1}}{^{n} C_{r + 1} +^{n} C_{r + 2}}$ $&^{n} C_{r} +^{n} C_{r - 1} =^{n + 1} C_{r}$ $\Rightarrow$ $v = \underset{r = r}{\sum^{r + 1}} \frac{n! r! (n - r + 1)!}{(r - 1)! (n - r + 1)! (n + 1)!}$ $= \frac{r}{n + 1} + \frac{r + 1}{n + 1} = \frac{2 r + 1}{n + 1} .$
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