Question

A=\(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}...+\dfrac{1}{2013.2015}\)

  giúp mình với nha. CẢm ơn mọi người rất nhiều

Answer 1

Ta có: A=\(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+....+\dfrac{1}{2013.2015}\)

\(\Leftrightarrow2A=2\left(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{2013.2015}\right)\)

\(\Leftrightarrow2A=\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{2021}-\dfrac{1}{2013}+\dfrac{1}{2013}-\dfrac{1}{2015}\)

\(\Leftrightarrow2A=\dfrac{1}{3}-\dfrac{1}{2015}=\dfrac{2012}{6045}\)

\(\Leftrightarrow A=\dfrac{1006}{6045}\)

Answer 2

2A=\(\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{1}{2013.2015}\)

2A=\(\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{2013}+\dfrac{1}{2015}\)

2A=\(\dfrac{1}{1}-\dfrac{1}{2015}\)

2A=\(\dfrac{2014}{2015}\)

 A=\(\dfrac{1007}{2015}\)

                     Khi gặp bài này, bn nên tách 1 phân số ra thành hiệu của 2 phân số.

 

Answer 3

Giải:

A=1/1.3+1/3.5+1/5.7+...+1/2013.2015

A=1/2.(2/1.3+2/3.5+2/5.7+...+2/2013.2015)

A=1/2.(1/1-1/3+1/3-1/5+1/5-1/7+...+1/2013-1/2015)

A=1/2.(1/1-1/2015)

A=1/2.2014/2015

A=1007/2015

Chúc bạn học tốt!

Answer 4

2A=2/1.3 + 2/3.5 + 2/5.7+....+2/2013.2015

2A=1-1/3+1/3-1/5+1/5-1/7+......+1/2013+1/2015

     =1-1/2015

=>2A=1-1/2015

=>2A=2014/2015

=>A=2014/2015 :2=2014/2015.1/2

=>A=2014/4030=1007/2015

Vậy A=1007/2015

Answer 5

Bạn cho mình sửa lại bài khi nãy nhé:

Ta có: \(A=\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{2013.2015}\)

\(\Rightarrow2A=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+..+\dfrac{2}{2013.2015}\)

\(\Leftrightarrow2A=\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{2013}-\dfrac{1}{2015}\)

\(\Leftrightarrow2A=\dfrac{1}{1}-\dfrac{1}{2015}=\dfrac{2014}{2015}\)

\(\Rightarrow A=\dfrac{1007}{2015}\)

Nãy mình sai chỗ mà rút gọn ấy, nhìn nhầm:vv tưởng là bắt đầu từ \(\dfrac{1}{3}\) cơ:vv

Answer 6

Ta có: \(A=\dfrac{1}{1\cdot3}+\dfrac{1}{3\cdot5}+\dfrac{1}{5\cdot7}+...+\dfrac{1}{2013\cdot2015}\)

\(=\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+...+\dfrac{2}{2013\cdot2015}\right)\)

\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{2013}-\dfrac{1}{2015}\right)\)

\(=\dfrac{1}{2}\left(1-\dfrac{1}{2015}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{2014}{2015}\)

\(=\dfrac{1007}{2015}\)