dễ thế mà mày ko bít làm à

B=2(2/3.5 - 2/ 5.7 +....................+ 2/99.101) 

B=2(1/3.5 -2/5.7+..............+1/99.100)

B=2(1/3-1/5+1/5-.............+1/99-1/100)

B=2(1/3-1/100)

B=2.97/100

B=97/50

Sửa đề: \(A=\frac{4}{3\cdot5}-\frac{6}{5\cdot7}+\frac{8}{7\cdot9}-\frac{10}{9\cdot11}+\cdots+\frac{100}{99\cdot101}\)

\(=\frac12\left(\frac{8}{3\cdot5}-\frac{12}{5\cdot7}+\frac{16}{7\cdot9}-\frac{20}{9\cdot11}+\cdots+\frac{200}{99\cdot101}\right)\)

\(=\frac12\left(\frac13+\frac15-\frac15-\frac17+\cdots+\frac{1}{99}+\frac{1}{101}\right)\)

\(=\frac12\left(\frac13+\frac{1}{101}\right)=\frac12\cdot\frac{104}{303}=\frac{52}{303}\)

A = 1/1.3 + 1/3.5 + 1/5.7 + ... + 1/2017.2019

A = 1/2 (1 - 1/3 + 1/3 - 1/5 + 1/5 - ... - 1/2019)

A = 1/2 (1 - 1/2019)

A = 1/2 . 2018/2019

A = 1009/2019

@Cỏ

\(A=\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+...+\frac{1}{2017\cdot2019}\)

\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2017}-\frac{1}{2019}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{2019}\right)=\frac{1}{2}\cdot\frac{2018}{2019}\)

\(=\frac{1009}{2019}\)

Mik giải phía dưới rồi đó. Câu lúc nãy bạn đăng ý