Question

​​1/1.3+1/3.5+1/5.7+...+1/99.101

Answer 1

A=1/1x3+1/3x5+1/5x7+...+1/99x101

gấp cả 2 vế lên 2 lần ta có:

Ax2=2/1x3+2/3x5+2/5x7+...+2/99x101

Ax2=1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101

Ax2=1-1/101

Ax2=100/101

A=100/101:2=50/101

Answer 2

\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{99.101}\)

\(=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}\)

\(=1-\frac{1}{101}\)

\(=\frac{100}{101}\)

Chúc bạn học tốt nha !!!