The sum of coefficient in the expansion of `(1+a d-2x^2)^n` is positive, when `a<1a n dn=2k ,k in N` negative, when `a<1a n dn=2k+1,k in N` positive, when `a<1a n dn in N` zero, when `a=1`

Options

A. positive, when `a lt 1` and `n = 2k, k in N`
B. negative, when `a lt 1` and `n = 2k + 1 , k in N`
C. positive, when `a gt 1` and `n in N`
D. zero, when `a = 1`

Answer

A, B, C, D

Explanation

To get the sum of coefficient,we put `x = 1`.
The, sum of coefficient in `(1+ax - 2x^(2))^(n)` is `(a-1)^(n)`
Obviously, when `a gt 1`sum is positive for any n.