Let [x] denote greatest integer less than or equal to x. If for n ∈ N,

Question

Let [x] denote greatest integer less than or equal to x. If for n ∈ \(\mathbb N,\) \((1-x+x^3)^n\) = \(\displaystyle\sum_{j=0}^{3n} a_jx^j,\) then \(\displaystyle\sum_{j=0}^{\big[\frac{3n}{2}\big]} a_{2j}+4\displaystyle\sum_{j=0}^{\big[\frac{3n-1}{2}\big]} a_{2j}+1\) is equal to :

(1) 2

(2) \(2^{n-1}\)

(3) 1

(4) n

Answer 1

Correct answer is (3)