\(S=\frac{3}{\left(1.2\right)^2}+\frac{5}{\left(2.3\right)^2}+...+\frac{61}{\left(30.31\right)^2}\)
\(S=\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+...+\frac{61}{30^2.31^2}\)
\(S=\frac{3}{1.4}+\frac{5}{4.9}+...+\frac{61}{900.961}\)
\(S=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{9}+...+\frac{1}{900}-\frac{1}{961}\)
\(S=1-\frac{1}{961}\)
\(S=\frac{960}{961}\)