Summing ${\frac{1}{n^2}}$ over subsets of $N$.

Yes to both cases: 1) $\frac{1}{15^2}+\frac{1}{20^2}=\frac{1}{12^2}$ 2) $\frac{1}{15^2}+\frac{1}{150^2}+\frac{1}{1500^2}+...+\frac{1}{20^2}+\frac{1}{200^2}+\frac{1}{2000^2}+...=\frac{1}{12^2}+\frac{1}{120^2}+\frac{1}{1200^2}...$

for first case - if we have pythagorean triple (a,b,c), such that $a^2+b^2=c^2$, then: $\frac{1}{a^2 b^2}=\frac{1}{a^2 c^2}+\frac{1}{b^2 c^2}$