18. [10] Find the coefficient of $x^{6}$ in the expansion of
$$
(x+1)^{6} \cdot \sum_{i=0}^{6} x^{i}
$$
Answer: 64 Each term of $(x+1)^{6}$ can be multiplied by a unique power $x^{i}, 0 \leq i \leq 6$ to get a sixth degree term. So the answer is the sum of the coefficients of the terms of $(x+1)^{6}$, which is the same as substituting $x=1$ into this power to get $2^{6}=64$.