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S=4/1.5+4/5.9+...+4/2001.2005
S =1/1 - 1/5 + 1/5 -1/9 + ...+ 1/2001 - 1/2005
S = 1/1 - 1/2005
S = 2014/2015
Ta có :
4/1 . 5 + 4/5 . 9 + ...+ 4/2001 . 2005
= 1 - 1/5 + 1/5 - 1/9 + ...+ 1/2001 - 1/2005
= 1 - 1/2005
= 2004/2005
Tham khảo nha !!!
\(A=\dfrac{4}{1\cdot5}+\dfrac{4}{5\cdot9}+...+\dfrac{4}{2001\cdot2005}\)
\(A=1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-...+\dfrac{1}{2001}-\dfrac{1}{2005}\)
\(A=1-\dfrac{1}{2005}=\dfrac{2004}{2005}\)
\(B=\dfrac{3}{10\cdot12}+\dfrac{3}{12\cdot14}+...+\dfrac{3}{998\cdot1000}\)
\(\dfrac{2}{3}B=\dfrac{2}{10\cdot12}+...+\dfrac{2}{998\cdot1000}\)
\(\dfrac{2}{3}B=\dfrac{1}{10}-\dfrac{1}{12}+\dfrac{1}{12}-...+\dfrac{1}{998}-\dfrac{1}{1000}\)
\(\dfrac{2}{3}B=\dfrac{1}{10}-\dfrac{1}{1000}=\dfrac{99}{1000}\)
\(B=\dfrac{99}{1000}:\dfrac{2}{3}=\dfrac{297}{2000}\)
\(A=\dfrac{4}{1.5}+\dfrac{4}{5.9}+...+\dfrac{4}{2001.2005}\)
\(\Rightarrow A=4\left(\dfrac{1}{1.5}+\dfrac{1}{5.9}+...+\dfrac{1}{2001.2005}\right)\)
\(\Rightarrow A=4.\dfrac{1}{4}\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{2001}-\dfrac{1}{2005}\right)\)
\(\Rightarrow A=1-\dfrac{1}{2005}\)
\(\Rightarrow A=\dfrac{2004}{2005}\)
\(S=\frac{5-1}{1.5}+\frac{9-5}{5.9}+\frac{13-9}{9.13}+..+\frac{2005-2001}{2001.2005}\)
\(=\left(1-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{9}\right)+\left(\frac{1}{9}-\frac{1}{13}\right)+...+\left(\frac{1}{2001}-\frac{1}{2005}\right)\)
\(=1+\left(-\frac{1}{5}+\frac{1}{5}\right)+\left(-\frac{1}{9}+\frac{1}{9}\right)+...+\left(-\frac{1}{2001}+\frac{1}{2001}\right)-\frac{1}{2005}\)
\(=1-\frac{1}{2005}\)
\(=\frac{2004}{2005}\)
$\dfrac{4}{1.4}+\dfrac{5.9}+....+\dfrac{4}{2001.2005}$
$=1+\dfrac15-\dfrac19+....+\dfrac{1}{2001}-\dfrac{1}{2005}$
$=1-\dfrac{1}{2005}=\dfrac{2004}{2005}$
\(\dfrac{4}{1.4}+\dfrac{4}{5.9}+...+\dfrac{4}{2001.2005}\)
\(=1+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{2001}-\dfrac{1}{2005}\)
\(=1+\dfrac{1}{5}-\dfrac{1}{2005}\)
\(=1+\dfrac{401}{2005}-\dfrac{1}{2005}\)
\(=1+\dfrac{400}{2005}=1+\dfrac{80}{401}=\dfrac{481}{401}\)
\(\dfrac{2}{1.5}\)+\(\dfrac{2}{5.9}\)+\(\dfrac{2}{9.13}\)+.................+\(\dfrac{2}{2013+2017}\)
=\(\dfrac{1}{1}\)-\(\dfrac{1}{5}\)+\(\dfrac{1}{5}\)-\(\dfrac{1}{9}\)+\(\dfrac{1}{9}\)-\(\dfrac{1}{13}\)+...................+\(\dfrac{1}{2013}-\dfrac{1}{2017}\)
=\(\dfrac{1}{1}-\dfrac{1}{2017}\)
=\(\dfrac{2017}{2017}+\dfrac{-1}{2017}\)
=\(\dfrac{2016}{2017}\)
\(D=4\left(\frac{4}{1.5}+\frac{4}{5.9}+...+\frac{4}{201.205}\right)\)
\(D=4\left(\left(1-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{9}\right)+...+\left(\frac{1}{201}-\frac{1}{205}\right)\right)\)
D=4[(1-1/205)
D=4.204/205
=>D=816/205
____________________--
li-ke cho mình nhé bn Cao Minh Hoàng
2A=\(\frac{4}{1.5}+\frac{4}{5.9}+...+\frac{4}{2001.2005}\)
2A=\(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+...+\frac{1}{2001}-\frac{1}{2005}\)
2A=1-\(\frac{1}{2005}\)=\(\frac{2004}{2005}\)
A=\(\frac{2004}{2005}:2\)=\(\frac{1002}{2005}\)
\(A=\frac{2}{1.5}+\frac{2}{5.9}+...+\frac{2}{2001.2005}\)\(=\frac{1}{2}\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+...+\frac{1}{2001}-\frac{1}{2005}\right)\)\(=\frac{2}{4}\left(\frac{4}{1.5}+\frac{4}{5.9}+...+\frac{4}{2001.2005}\right)\)\(=\frac{1}{2}\left(1-\frac{1}{2005}\right)=\frac{1}{2}.\frac{2004}{2005}=\frac{1002}{2005}\)
Câu B làm tương tự