Prove that the middle term in the expansion of `(1+x)^(2n)` is `(1xx3xx5xx….xx(2n-1)xx2^nx^n)/(lfloorn)`

Show that the middle term in the expansion of (1+x)^(2n) is (1.3.5….(2n-1))/(n!) 2^(n)x^(n) , where n is a positive integer.

Find the middle terms in the expansion of : (x/y+y/x)^(2n+1) .

Write the middle term in the expansion of : (1+x)^(2n) , where n is a positive integer.

If the middle term in the expansion (x^(2)+1//x)^(n) is 924 x^(6) , then find the value of n.

Prove that the coefficient of x^n in the expansion of (1+x)^(2n) is twice the coefficient of x^n in the expansion of (1+x)^(2n-1)

Statement-1 The number of terms in the expansion of (x + (1)/(x) + 1)^(n) " is " (2n +1) Statement-2 The number of terms in the expansion of (x_(1) + x_(2) + x_(3) + …+ x_(m))^(n) "is " ^(n + m -1)C_(m-1) .

The number for the expansion 3xx10^(7)+2xx10^(2)+5xx10^(1) 3000025.

Find the value of [((1)/(2))^(2)]^(3)xx((1)/(3))^(-4)xx3^(-2)xx(1)/(6)

Statement-1 Greatest coefficient in the expansion of (1 + 3x)^(6) " is " ""^(6)C_(3) *3^(3) . Statement-2 Greatest coefficient in the expansion of (1 + x)^(2n) is the middle term .

Find the sum to n terms of the series given below:- 1xx2 + 2xx3 + 3xx4 + 4xx5 +...