1. (2 points) For the polynomial $\left(x^{2}-x+1\right)^{100}$, find the sum of the coefficients of the even powers of $x$.
Solution: Let $P(x)=\left(x^{2}-x+1\right)^{100}$. The desired sum is $\frac{P(1)+P(-1)}{2}=\frac{1+3^{100}}{2}$

Answer: $\frac{1+3^{100}}{2}$