If the coefficients of (2r + 1)th term and (r + 2)th term in the expansion of (1 + x)⁴³ are equal, find r.

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Solution

$Given : - (1 + x)^{43} We know that the coefficient of the r th term in the expansion of (1 + x)^{n} is {}^{n}C_{r - 1} Therefore, the coefficients of the (2 r + 1) th and (r + 2) th term s in the given expression are {}^{43}C_{2 r + 1 - 1} and {}^{43}C_{r + 2 - 1} For these coefficients to be equal, we must have : \Rightarrow 2 r = r + 1 or, 2 r + r + 1 = 43 [∵ {}^{n}C_{r} = {}^{n}C_{s} \Rightarrow r = s or r + s = n] \Rightarrow r = 14 [∵ for r = 1 it gives the same term]$

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If the coefficients of (2r+1)th term and (r+2)th terms in the expansion of $(1 + x)^{43}$ are equal, find r.

If the coefficient of (2r + 1)th term and (r + 2)th term are equal in expansion of $(1 + x)^{43}$ , then r =

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