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20 tháng 3 2018

\(B=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{2017.2019}\)

\(2B=\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{2017.2019}\)

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

\(2B=\frac{1}{1}-\frac{1}{2019}\)

\(2B=\frac{2018}{2019}\)

\(\Rightarrow B=\frac{2018}{2019}:2\Rightarrow B=\frac{1009}{2019}\)

20 tháng 3 2018

\(B=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+.....+\frac{2}{2017.2019}\right)\)

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

\(=\frac{1}{2}\left(1-\frac{1}{2019}\right)=\frac{1009}{2019}\)

=1/2(2/1*3+2/3*5+...+2/2017*2019)

=1/2(1-1/3+1/3-1/5+...+1/2017-1/2019)

=1/2*2018/2019

=1009/2019

11 tháng 4 2023

=1/2(2/1x3+2/3x5+...+2/2017x2019)

=1/2(1-1/3+1/3-1/5+...+1/2017-1/2019)

=1/2x2018/2019

=1008/2019

20 tháng 3 2018

xem trên mạng

20 tháng 3 2018

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

=1/2.(2/1.3+2/3.5+...+2/2017.2019)

=1/2.[(1-1/3)+(1/3-1/5)+...+(1/2017-1/2019)]

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

=1/2.2018/2019

=2017/403

=1009/2019

tk cho mk nhe

1 tháng 6 2020

\(2.S=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2017.2019}\)

\(=\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+...+\frac{2019-2017}{2017.2019}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2017}-\frac{1}{2019}\)

\(=1-\frac{1}{2019}=\frac{2018}{2019}\)

=> \(S=\frac{1009}{2019}\)

Tính: S= 1/1.3 + 1/3.5 +1/5.7 + 1009/2019 .....+ 1/2017.2019

Trả lời:

1009/2019

Cố gắng lên (tự nhủ) 

\(S=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2017.2019}\)

\(2S=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2017}-\frac{1}{2019}\)

\(2S=1-\frac{1}{2019}=\frac{2018}{2019}\)

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

19 tháng 4 2023

Hi

22 tháng 3 2017

\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2017.2019}\)

\(=1-\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+..+\frac{1}{2017}-\frac{1}{2019}\div2\)

\(=\left(1-\frac{1}{2019}\right)\div2\)

\(=\frac{2018}{2019}\div2\)

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

22 tháng 3 2017

Đặt \(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2017.2019}\)

\(2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2017.2019}\)

\(2A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2017}-\frac{1}{2019}\)

\(2A=1-\frac{1}{2017}\)

\(2A=\frac{2016}{2017}\)

\(A=\frac{2016}{2017}:2\)

\(A=\frac{1008}{2017}\)

8 tháng 8 2021

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

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

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

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

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

16 tháng 4 2019

A=1/1*3+1/3*5+...+1/2017*2019

2A=2/1*3+2/3*5+...+2/2017*2019

2A=1-1/3+1/3-1/5+..+1/2017-1/2019

2A=1-1/2019

2A=2018/2019

A=(2018/2019):2

A=1009/2019

16 tháng 4 2019

A=1009/2019

\(M=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2017.2019}\)

\(=\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2017}-\frac{1}{2019}\right)\)

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

\(=\frac{1}{2}.\frac{2018}{2019}\)

\(=\frac{2018}{4038}\)

\(\Rightarrow\frac{2018}{4038}< \frac{1}{2}\)( lấy máy tính ) 

18 tháng 12 2019

\(M=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+.....+\frac{1}{2017.2019}\)

\(\Rightarrow M=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-......-\frac{1}{2017}+\frac{1}{2017}-\frac{1}{2019}\)

\(\Rightarrow M=1-\frac{1}{2019}\)

\(\Rightarrow M=\frac{2019}{2019}-\frac{1}{2019}\)

\(\Rightarrow M=\frac{2018}{2019}\)

Có \(\frac{2018}{2019}=\frac{2018.2}{2019.2}=\frac{4036}{4038}\)

\(\frac{1}{2}=\frac{1.2019}{2.2019}=\frac{2019}{4038}\)

Mà \(\frac{4036}{4038}< \frac{2019}{4038}\Rightarrow M< \frac{1}{2}\)

Vậy M < \(\frac{1}{2}\)

4 tháng 4 2019

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