Comment on the binomial series for `(1+x)^m` when x = - 2 and m =-1 .

Multiply the binomials. (x-4) and (2x + 3)

The fourth term in the binomial expansion of (x^2-1/x^3)^n is independent of x, when n is equal to:

Expand using Binomial Theorem (1+x/2-2/x)^4 , x ne 0 .

The number of integral values of m for which the x-coordinate of the point of intersection of the lines 3x+4y=9 and y=m x+1 is also an integer is (a) 2 (b) 0 (c) 4 (d) 1

Prove that (-a,-a/2) is the orthocentre of the triangle formed by the lines y = m_(i) x + a/(m_(i)) , I = 1,2,3, m_(1) m_(2) m_(3) being the roots of the equation x^(3) - 3x^(2) + 2 = 0

Multiply the binomials. (2.5m - 0.5n) and (2.5 m + 0.5n)

Find the sum to n terms of the following series : 1+2x+ 3x^2+4x^3+ .......... when |x|<1.

Expand (1-x/2)^(-1//2) when | x | < 2.

Find the sum to n terms of the following series : 1+ 3x+ 5x^2+7x^3+ .......... when |x|<1.