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r and n are positive integers r gt 1,n g...

`r` and `n` are positive integers `r gt 1`,`n gt 2` and coefficient of `(r + 2)^(th)` term and `3r^(th)` term in the expansion of `(1 + x)^(2n)` are equal, then `n` equals

A

`n = 2r`

B

`n = 2r + 1`

C

`n = 3r`

D

None of these

Text Solution

Verified by Experts

In the expansion `(1+x)^2n,t_(3r)=.^2nC_(3r-1)(x)^(3r+1)`.
and `t_(r+2)= .^2nC_r+1(x)^(r-1)`
Since, binomial coefficients of `t_3r and t_(r+2)` are equal.
`therefore .^2nC_(3r-1)=.^2nC_r+1`
`rArr 3r-1= 1 or 2n=(3r-1)+(r+1)`
` rArr 2r=2 or 2n =4r`
`rArr r=1 or n=2r`
But `r gt 1`
`therefore` We take , `n=2r`.
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