Question

please answer 12 th sum

Answer 1

Option(D) - 31

Given, (1+x-2x^2) = 1+a1x + a2x^2 + a3x^3 + ...... +a12x^12    ------ (1)

Substitute x = 1 in equation (1), we get

0 = 1+a1+a2+a3+........+a12    ------------- (2)

Substitute x=-1 in equation (1), we get

2^6 = 1-a1+a2-a3+.....+a12     ------------ (3)

On solving (2) and (3) we get

2^6 = 2(1+a2+a4+....+a12)

a2+a4+...+a12 = 2^5-1

                       = 32 - 1

                       = 31.