Question

A=1 1 1. 1

— + — + — +.... + ——

1.3 3.5 5.7. 2011.2013

Bài trên yêu cầu : Tính.

Các anh chị giúp em vs ạ. Em cảm ơn tốc 😊

Answer 1

đề bài sải rồi

Answer 2

\(A=\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{2011.2013}\)

\(=\dfrac{1}{2}\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{2011.2013}\right)\)

\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{2011}-\dfrac{1}{2013}\right)\)

\(=\dfrac{1}{2}\left(1-\dfrac{1}{2013}\right)\)

\(=\dfrac{1}{2}.\dfrac{2012}{2013}\)

\(=\dfrac{1006}{2013}\)

Answer 3

Ý bạn là: \(A=\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{2011.2013}\)

Lời giải:\(A=\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{2011+2013}\)

\(\Rightarrow A=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{2011}-\dfrac{1}{2013}\)

\(\Rightarrow A=1-\dfrac{1}{2013}\)

\(\Rightarrow A=\dfrac{2012}{2013}\)