If-the-coefficient-of-the-middle-term-in-the-expansion-of-the-1-x-2n-2-is-p-and-the-coefficients-of-middle-terms-in-the-expansion-of-1-x-2n-1-are-q-and-r-then-

Question Number 18168 by allizzwell last updated on 16/Jul/17

If the coefficient of the middle term in

the expansion of the {(1 + x)}^{2 n + 2} is p and

the coefficients of middle terms in the

expansion of {(1 + x)}^{2 n + 1} are q and r, then

Answered by ajfour last updated on 16/Jul/17

p =^{2 n + 2} C_{n + 1}

q =^{2 n + 1} C_{n} = r =^{2 n + 1} C_{n + 1}

further^{2 n + 2} C_{n + 1} = \frac{2 n + 2}{n + 1}^{2 n + 1} C_{n}

\Rightarrow p = 2 q = 2 r .

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