1,
a, $M=5+5^2+5^3+...+5^{90}$
$⇒M=5(1+5+5^2)+...+5^{88}.(1+5+5^2)$
$⇒M=5.31+...+5^{88}.31$
$⇒M=31.(1+...+5^{88})\vdots 31$
$⇒M\vdots 31$
3, $N=\frac{1}{4^2}+$ $\frac{1}{6^2}+...+$ $\frac{1}{(2n)^2}$
$⇒N<\frac{2}{4.6}+$ $\frac{2}{6.8}+...+$ $\frac{2}{2n.(2n+2)}$
$⇒N<\frac{1}{4}-$ $\frac{1}{6}+$ $\frac{1}{6}-$ $\frac{1}{8}+...+$ $\frac{1}{2n}-$ $\frac{1}{2n+2}$
$⇒N<\frac{1}{4}-$ $\frac{1}{2n+2}<$ $\frac{1}{4}$
