Solve $\sum_{i=1}^{200} {1\over{1+x_i}} =?$

Question

$$ (x^{2}+x+1)^{100}=a_0+a_1x+a_2x^{2}+...+a_{199}x^{199}+a_{200}x^{200}$$ $$\sum_{i=1}^{200} {1\over{1+x_i}} =?$$ Can somebody help me? Thank you!

Answer 1

$$\sum_{k=1}^{200}\frac{1}{1+x_k}=100\left(\frac{1}{1+x_1}+\frac{1}{1+x_2}\right)=\frac{100(2+x_1+x_2)}{1+x_1+x_2+x_1x_2}=$$ $$=\frac{100(2-1)}{1-1+1}=100.$$