\(M=\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}\)\(\)
\(M=\frac{2}{3}-\frac{2}{5}+\frac{2}{5}-\frac{2}{7}+...+\frac{2}{97}-\frac{2}{99}\)
\(M=\frac{2}{3}-\frac{2}{99}\)
\(M=\frac{64}{99}\)
\(2M=\left(\frac{2}{3}-\frac{2}{5}\right)+\left(\frac{2}{5}-\frac{2}{7}\right)+\left(\frac{2}{7}-\frac{2}{9}\right)+...+\left(\frac{2}{97}-\frac{2}{99}\right)\)
\(2M=\frac{2}{3}-\frac{2}{5}+\frac{2}{5}-\frac{2}{7}+\frac{2}{7}-\frac{2}{9}+...+\frac{2}{97}-\frac{2}{99}\)
\(2M=\frac{2}{3}-\left(\frac{2}{5}-\frac{2}{5}\right)-\left(\frac{2}{7}-\frac{2}{7}\right)-...-\left(\frac{2}{97}-\frac{2}{97}\right)-\frac{2}{99}\)
\(2M=\frac{2}{3}-\frac{2}{99}\)
\(2M=\frac{64}{99}\)
\(M=\frac{32}{99}\)
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