Question

1/1*3+1/3*5+.....1/119*121

 

Answer 1

Đặt A=1/1*3+1/3*5+...+1/119*121

2A=2/1*3+2/3.5+...+2/119.121

2A=1-1/3+1/3-1/5+...+1/119-1/121

2A=1-1/121

2A=120/121

A=60/121

Answer 2

\(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{119.121}\)

\(=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{119.12}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{119}-\frac{1}{121}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{121}\right)\)

\(=\frac{1}{2}.\frac{120}{121}\)

\(=\frac{60}{121}\)