# Math Help - Summation

1. ## Summation

$\prod_{n=1}^{1996}(1+nx^{3^n})=1 + \sum_{i=1}^{m} a_i x^{k_i}$

Find $a_{1996}$.

2. We have to find the coefficient of $x^{1996}$ in the left member.

The powers of x in the left member are of the form $x^{\displaystyle 3^{k_1}+3^{k_2}+\ldots+3^{k_l}}=x^{3p}$

But 1996 is not divisible to 3. So the coefficient is 0.

3. Thanks what about if $k_1 (That sum has $m$ terms).

$a_1, a_2, a_3... a_m$ are non-zero.