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Given positive integers r>1,n> 2, n bei...

Given positive integers `r>1,n> 2, n` being even and the coefficient of `(3r)th` term and `(r+ 2)th` term in the expansion of `(1 +x)^(2n)` are equal; find r

A

`n = 2r`

B

`n = 3r`

C

`n = 2r + 1`

D

None of these

Text Solution

AI Generated Solution

To solve the problem, we need to find the value of \( r \) given that the coefficients of the \( (3r) \)th term and the \( (r + 2) \)th term in the expansion of \( (1 + x)^{2n} \) are equal. ### Step-by-step Solution: 1. **Identify the general term in the binomial expansion**: The general term \( T_k \) in the expansion of \( (1 + x)^{2n} \) is given by: \[ T_k = \binom{2n}{k-1} x^{k-1} ...
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