Question 22
If we have
$$(1-3x)+(1-3x)^2+\cdots+(1-3x)^{100}=a_0+a_1x+a_2x^2+\cdots+a_{100}x^{100},$$
for some integers $a_0,a_1,\ldots,a_{100}$, what is the value of
$$\left|\frac{a_1}{3}+\frac{a_2}{3^2}+\cdots+\frac{a_{100}}{3^{100}}\right|?$$
$$(1-3x)+(1-3x)^2+\cdots+(1-3x)^{100}=a_0+a_1x+a_2x^2+\cdots+a_{100}x^{100},$$
for some integers $a_0,a_1,\ldots,a_{100}$, what is the value of
$$\left|\frac{a_1}{3}+\frac{a_2}{3^2}+\cdots+\frac{a_{100}}{3^{100}}\right|?$$