Find 100-th derivative of $1/(x^2+x+1)$ at x = 0

Question

The hint is using power series. So I use Taylor's formula but still cannot reduce it. Any other hints?

Answer 1

Notice that $$\frac1{1+x+x^2}=\frac{1-x}{1-x^3}=(1-x)(1+x^3+x^6+\cdots).$$