The equatin `2x = (2n +1)pi (1 - cos x) ,` (where n is a positive integer)

Prove that the function f(x)=x^n is continuous at x = n , where n is a positive integer.

The number of non-negative integral solution x_1 + x_2 + x_3 + x_4 <=n (where n is a positive integer) is :

If A= [(3 , -4), (1 , -1) ] , then prove that A^n=[(1+2n , -4n), (n , 1-2n) ] , where n is any positive integer.

The value of the integral int_(0)^(pi//2) sin 2n x cot x dx, where n is a positive integer, is

If the first three terms in the expansion of (1 -ax)^n where n is a positive integer are 1,-4x and 7x^2 respectively then a =

The number non-negative integral solutions of x_(1)+x_(2)+x_(3)+x_(4) le n (where n is a positive integer) is:

If two consecutive terms in the expansion of (x+a)^n are equal to where n is a positive integer then ((n+1)a)/(x+a) is

Prove that 2^n >1+nsqrt(2^(n-1)),AAn >2 where n is a positive integer.

By using binomial theorem prove that (2^(3n)-7n-1) is divisible by 49 where n is a positive integer.

Prove that (^n C_0)/x-(^n C_0)/(x+1)+(^n C_1)/(x+2)-+(-1)^n(^n C_n)/(x+n)=(n !)/(x(x+1)(x-n)), where n is any positive integer and x is not a negative integer.