Question

Giúp mk bài này nhé, ko đc trêu gì cả. I help me!

Bài4: Chứng minh

1/1.2 +1/3.4 +1/5.6 +1/6.7 +...+ 1/49.50= 1/26 +1/27 +...+ 1/50

 

Answer 1

Ta có

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

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

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

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

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

=> \(\frac{1}{1.2}+\frac{1}{3.4}+....+\frac{1}{49.50}\)\(=\frac{1}{26}+\frac{1}{27}+....+\frac{1}{50}\)