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27 tháng 3 2016

1/1.3+1/5.7+1/7.9+.....+1/13.15

=1-1/3+1/5-1/7+1/7-1/9+............+1/13-1/15

=1-1/15

=14/15

27 tháng 3 2016

đề thiếu hay sao ấy bạn

25 tháng 2 2017

2.

\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{\left(2x+1\right).\left(2x+3\right)}=\frac{15}{93}\)

\(\Rightarrow\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}\right)+\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{7}\right)+\frac{1}{2}.\left(\frac{1}{7}-\frac{1}{9}\right)+...+\frac{1}{2}.\left(\frac{1}{2x+1}-\frac{1}{2x+3}\right)=\frac{15}{93}\)

\(\Rightarrow\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{2x+1}-\frac{1}{2x+3}\right)=\frac{15}{93}\)

\(\Rightarrow\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{2x+3}\right)=\frac{15}{93}\)

\(\Rightarrow\frac{1}{3}-\frac{1}{2x+3}=\frac{15}{93}:\frac{1}{2}\)

\(\Rightarrow\frac{1}{3}-\frac{1}{2x+3}=\frac{10}{31}\)

\(\Rightarrow\frac{1}{2x+3}=\frac{1}{3}-\frac{10}{31}\)

\(\Rightarrow\frac{1}{2x+3}=\frac{1}{93}\)

\(\Rightarrow\)2x + 3 = 93

\(\Rightarrow\)2x = 93 - 3

\(\Rightarrow\)2x = 90

\(\Rightarrow\)x = 90 : 2 = 45

25 tháng 2 2017

\(H=\frac{3}{1.5}+\frac{3}{5.9}+\frac{3}{9.13}+...+\frac{3}{33.37}\)

\(\frac{3}{4}\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{33}-\frac{1}{37}\right)\)

\(\frac{3}{4}\left(1-\frac{1}{37}\right)\)

\(\frac{3}{4}.\frac{36}{37}=\frac{27}{37}\)

5 tháng 4 2018

Ta có: \(N=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{2005.2006}\)

\(\Rightarrow N=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{2005}-\frac{1}{2006}\)

          \(=1-\frac{1}{2006}=\frac{2005}{2006}\)

 \(M=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+....+\frac{2}{2015.2017}\)

      \(\Rightarrow1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{2015}-\frac{1}{2017}\)

        \(=1-\frac{1}{2017}=\frac{2016}{2017}\)

5 tháng 4 2018

N = 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +...+ 1/2005 - 1/2006

   = 1/1 - 1/2006

   = 2006/2006 - 1/2006

   =  2005/2006

5 tháng 7 2016

Ta có: \(A=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{13.15}\)

\(\Rightarrow2A=\frac{2}{3.5}+\frac{2}{5.7}+..+\frac{2}{13.15}\)

\(\Rightarrow2A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\)

\(\Rightarrow2A=\frac{1}{3}-\frac{1}{15}=\frac{4}{15}\)

\(\Rightarrow A=\frac{4}{15}:2=\frac{2}{15}\)

9 tháng 8 2021

\(A=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{13.15}\)

\(2A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{13.15}\)

\(2A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{13}-\frac{1}{15}\)

\(2A=\frac{1}{3}-\frac{1}{15}=\frac{4}{15}\)

\(\Rightarrow A=\frac{4}{15}:2=\frac{2}{15}\)

5 tháng 7 2016

\(\Rightarrow A=\frac{1}{2}.\left(\frac{2}{3.5}+\frac{2}{5.7}+......+\frac{2}{13.15}\right)\)

\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+............+\frac{1}{13}-\frac{1}{15}\right)\)

\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{15}\right)\)

\(\Rightarrow A=\frac{1}{2}.\frac{4}{15}\)

\(\Rightarrow A=\frac{2}{15}\)

5 tháng 7 2016

kcj

22 tháng 8 2020

\(A=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{13.15}=\frac{1}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{13.15}\right)\)

\(=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\right)=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{15}\right)=\frac{1}{2}.\frac{4}{15}=\frac{2}{15}\)

22 tháng 8 2020

\(A=\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+...+\frac{1}{13\cdot15}=\frac{1}{2}\left(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{13\cdot15}\right)\)

\(=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\right)\)

\(=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{15}\right)=\frac{1}{2}\cdot\frac{4}{15}=\frac{2}{15}\)

quy luật +3+5+7+9+11+........

10 tháng 2 2016

bai toan nay kho

5 tháng 4 2016

Mk bik câu B nè!

2B = 2/3.5 + 2/5.7 + 2/7.9 +.......+2/97.99

2B = 1/3 - 1/5 + 1/5 - 1/7 +.......+ 1/97 - 1/99

2B = 1/3 - 1/99

2B = 32/99

=> B = 16/99 

5 tháng 4 2016

Bạn có chắc là đúng ko vậy

23 tháng 4 2015

\(D=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+......+\frac{1}{29.31}\)

\(\Rightarrow D=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}\right)+\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{7}\right)+......+\frac{1}{2}.\left(\frac{1}{29}-\frac{1}{31}\right)\)

\(\Rightarrow D=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{31}\right)\)

\(\Rightarrow D=\frac{1}{2}.\frac{28}{93}=\frac{14}{94}\)

NHỚ LIKE CHO MÌNH NHA ^_^