Question

1/1.2+1/3.4+...+1/49.50=1/26+1/27+...+1/50

Chứng mih 2 vế bằng nhau

Answer 1

Ta có:\(\frac{1}{1.2}+\frac{1}{3.4}+......+\frac{1}{49.50}\)

\(=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+.........+\frac{1}{49}-\frac{1}{50}\)

\(=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+..........+\frac{1}{50}-2.\left(\frac{1}{2}+\frac{1}{4}+....+\frac{1}{50}\right)\)

\(=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+........+\frac{1}{50}-\left(1+\frac{1}{2}+.....+\frac{1}{25}\right)\)

\(=\frac{1}{26}+\frac{1}{27}+....+\frac{1}{50}\)

\(\Rightarrowđpcm\)