Given the integers $r>1$ , $n>2$ and co-efficient of ${\left( {3r} \right)^{th}}$ and ${\left( {r + 2} \right)^{th}}$ term in the binomial expansion of ${\left( {1 + x} \right)^{2n}}$ are equal, then

কাজু বাদাম

=2nC3r−1x3r−1

and (r+2)th term in the expansion of (1+x)

=2nCr+1xr+1

Given that the binomial coefficients of (3r−1) and (r+2)th terms are equal.

Thus 2nC3r−1=2nCr+1

⇒3r−1=r+1

or 2n=(3r−1)+(r+1)

⇒2r=2 or 2n=4r

⇒r=1 or n=2r

But r>1

Therefore, n=2r

Given the integers r>1r>1r>1,n>2n>2n>2 and co-efficient of (3r)th{\left( {3r} \right)^{th}}(3r)th and (r+2)th{\left( {r + 2} \right)^{th}}(r+2)th term in the binomial expansion of (1+x)2n{\left( {1 + x} \right)^{2n}}(1+x)2n are equal, then