\(M=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{97.99}\)
\(\Rightarrow2M=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{97.99}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{97}-\frac{1}{99}\)
\(=\frac{1}{3}-\frac{1}{99}=\frac{32}{99}\)
\(\Rightarrow M=\frac{32}{99}:2=\frac{16}{99}\)
Vậy \(M=\frac{16}{99}\)
2M = 2/3*5 + 2/5*7 + ... + 2/97*99
2M = 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/97 - 1/99
2M = 1/3 -1/99
2M = 32/99
M =16/99
M=1/3-1/5+1/5-1/7+....+1/97-1/99
=1/3-1/99=32/99.
