Đặt \(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2015.2017}\), ta có:
\(A=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2015.2017}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2015}-\frac{1}{2017}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{2017}\right)\)
\(=\frac{1}{2}.\frac{2016}{2017}=\frac{1008}{2017}\)
\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+....+\frac{1}{2015.2017}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{2015}-\frac{1}{2017}+\frac{1}{2017}\)
\(=1-\frac{1}{2017}\)
\(=\frac{2016}{2017}\)
mk đầu tiên đấy
\(\text{Đặt }A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2015.2017}\)
\(\Rightarrow2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2015.2017}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2015}-\frac{1}{2017}\)
\(=1-\frac{1}{2017}\)
\(=\frac{2017-1}{2017}=\frac{2016}{2017}\)
\(\text{Vậy }A=\frac{2016}{2017}\).
=2.(1/1.3+1/3.5+1/5.7+...+1/2015.2017)
=1/1-1/3+1/3-1/5+1/5-1/7+...+1/2015-1/2017
=1-1/2017
=2016/2017
vì lúc đầu ta nhân 2 nên bây giờ ta chia 2
=2016/2017:2
=1008/2017
k nha mọi người
=1008/2017
cac ban lam rat dung giong y minh
Đặt \(A=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{2015.2017}\)
\(=>2A=2\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{2015.2017}\right)\)
\(=\frac{2}{1.3}+\frac{2}{3.5}+...\frac{2}{2015.2017}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2015}-\frac{1}{2017}\)
\(=\frac{1}{3}-\frac{1}{2017}=\frac{2017-3}{6051}=\frac{2014}{6051}\)
\(=>A=\frac{2014}{6051}:2=\frac{2014}{6051}.\frac{1}{2}=\frac{1007}{6051}\)
Vậy \(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{2015.2017}=\frac{1007}{6051}\)
ban nguyen thi lan huong oi cho mình hỏi \(\frac{1}{3}\)- \(\frac{1}{5}\)= \(\frac{2}{15}\) mà
\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2015.2017}\)( Gọi biểu thức trên là A )
Ta có :
A . 2 = \(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+.....+\frac{2}{2015.2017}\)
A. 2 = 1 - \(\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2015}-\frac{1}{2017}\)
A . 2 = 1 - \(\frac{1}{2017}\)
A . 2 = \(\frac{2016}{2017}\)
A = \(\frac{2016}{2017}:2\)
A = \(\frac{2016}{2017}.\frac{1}{2}\)
A = \(\frac{1008}{2017}\)
Cho mình sửa lại dòng cuối:
\(2A=\frac{2016}{2017}\)
\(\Rightarrow A=\frac{2016}{2017}:2=\frac{1008}{2017}\)
\(\text{Vậy A}=\frac{1008}{2017}\).
=1/2x(1/1-1/3)+(1/3-1/5)+(1/5-1/7)+....+(1/2015-1/2017)
=1/2x(1-1/2017)
=1/2x2016/2017=1008/2017
Bạn ơi mình ra 2018/2017 nhé .Đúng 10000000000000000000 %luôn đấy
