Question

mình sẽ tick cho ai trả lời

Answer 1

Bài 1: 

\(A=\dfrac{1}{2}\left(\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+...+\dfrac{2}{37\cdot39}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{37}-\dfrac{1}{39}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{13-1}{39}=\dfrac{1}{2}\cdot\dfrac{12}{39}=\dfrac{1}{2}\cdot\dfrac{6}{13}=\dfrac{3}{13}\)

Bài 2: 

\(B=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{95}-\dfrac{1}{96}\)

\(=\dfrac{1}{3}-\dfrac{1}{96}=\dfrac{31}{96}\)