Find the coefficient of ${x^9}$ in the expansion of $ (1 + x)( 1 + x^2)( 1 + x^3)..(1 + x^{100})$ Find the coefficient of ${x^9}$ in the expansion of $\left( {1 + x} \right)\left( {1 + {x^2}} \right)\left( {1 + {x^3}} \right)..\left( {1 + {x^{100}}} \right)$.
The official answer is 8.
How do I find the general term,
Dividing the above equation by $(1-x)$ is not generating the required result.

Hint:
$$\begin{align}9=9+0\\=8+1\\=7+2\\=6+3\\=6+2+1\\=5+4\\=5+3+1\\=4+3+2\end{align}$$
We don't have to worry about 4 summands, since $1+2+3+4>9$. There is no known closed form for the general term.
