If the sum of the coefficients of even powers of x in the expansion of (1-x+x^2 )^ 2 n is 3281 , then n =

Step-by-step solution

Let (1-x+x^2 )^ 2 n =a₀+a₁ x+a₂ x^2+ +a_ 2 n x^ 4 n put x=1 , we get 1^ 2 n =1= a ₀+ a ₁+ a ₂+ + a _ 2 n .....(i) Put x=-1 , we get 3^ 2 n =a₀-a₁+a₂- +a_ 2 n .....(ii) Adding equations (i) and (ii) we get 1+3^ 2 n =2 (a₀+a₂+ +a_ 2 n ) Given that sum of even power of x is 3281 aligned & 1+3^ 2 n =2 3281=6562 & 3^ 2 n =6561=3^8 2 n=8 n=4 aligned