\(A=\dfrac{4}{1\cdot5}+\dfrac{4}{5\cdot9}+...+\dfrac{4}{2001\cdot2005}\)

\(A=1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-...+\dfrac{1}{2001}-\dfrac{1}{2005}\)

\(A=1-\dfrac{1}{2005}=\dfrac{2004}{2005}\)

\(B=\dfrac{3}{10\cdot12}+\dfrac{3}{12\cdot14}+...+\dfrac{3}{998\cdot1000}\)

\(\dfrac{2}{3}B=\dfrac{2}{10\cdot12}+...+\dfrac{2}{998\cdot1000}\)

\(\dfrac{2}{3}B=\dfrac{1}{10}-\dfrac{1}{12}+\dfrac{1}{12}-...+\dfrac{1}{998}-\dfrac{1}{1000}\)

\(\dfrac{2}{3}B=\dfrac{1}{10}-\dfrac{1}{1000}=\dfrac{99}{1000}\)

\(B=\dfrac{99}{1000}:\dfrac{2}{3}=\dfrac{297}{2000}\)

\(A=\dfrac{4}{1.5}+\dfrac{4}{5.9}+...+\dfrac{4}{2001.2005}\)

\(\Rightarrow A=4\left(\dfrac{1}{1.5}+\dfrac{1}{5.9}+...+\dfrac{1}{2001.2005}\right)\)

\(\Rightarrow A=4.\dfrac{1}{4}\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{2001}-\dfrac{1}{2005}\right)\)

\(\Rightarrow A=1-\dfrac{1}{2005}\)

\(\Rightarrow A=\dfrac{2004}{2005}\)

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

a) A = 3/10.12 + 3/12.14 + ... + 3/998.1000

2/3.A = 2/10.12 + 2/12.14 + ... + 2/998.1000

2/3.A = 1/10 - 1/12 + 1/12 - 1/14 + ... + 1/998 - 1/1000

2/3.A = 1/10 - 1/1000

2/3.A = 99/1000

A = 99/1000 : 2/3

A = 99/1000 . 3/2

A = 297/2000

b) B = 2/1.4 + 2/4.7 + 2/7.10 + ... + 2/22.25

3/2.B = 3/1.4 + 3/4.7 + 3/7.10 + ... + 3/22.25

3/2.B = 1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + ... + 1/22 - 1/25

3/2.B = 1 - 1/25

3/2.B = 24/25

B = 24/25 : 3/2

B = 24/25 . 2/3

B = 16/25

Ủng hộ mk nha ^_-

a) Ta có: \(A=\frac{3}{10.12}+\frac{3}{12.14}+....+\frac{3}{998.1000}.\)

 \(\Rightarrow\frac{2}{3}A=\frac{1}{10.12}+\frac{1}{12.14}+...+\frac{1}{998.1000}\)

 \(\Rightarrow\frac{2}{3}A=\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}+...+\frac{1}{998}-\frac{1}{1000}\)

 \(\Rightarrow\frac{2}{3}A=\frac{1}{10}-\frac{1}{1000}=\frac{99}{1000}\)

 \(\Rightarrow A=\frac{99}{1000}:\frac{2}{3}=\frac{297}{2000}\)

S = \(\dfrac{1}{10.12}\) + \(\dfrac{1}{12.14}\) + .....+ \(\dfrac{1}{998.1000}\)

S = \(\dfrac{1}{2}\).( \(\dfrac{2}{10.12}\) + \(\dfrac{2}{12.14}\)+.....+ \(\dfrac{2}{998.1000}\))

S = \(\dfrac{1}{2}\).( \(\dfrac{1}{10}\)- \(\dfrac{1}{12}\)+ \(\dfrac{1}{12}\) - \(\dfrac{1}{14}\)+...+\(\dfrac{1}{998}\)- \(\dfrac{1}{1000}\))

S = \(\dfrac{1}{2}\). ( \(\dfrac{1}{10}\) - \(\dfrac{1}{1000}\))

S = \(\dfrac{1}{2}\).\(\dfrac{99}{1000}\)

S = \(\dfrac{99}{2000}\)

\(=\frac{2014}{2015}\)

tk mk nha

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 !!! 

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

\(S=\frac{5-1}{1.5}+\frac{9-5}{5.9}+\frac{13-9}{9.13}+..+\frac{2005-2001}{2001.2005}\)

\(=\left(1-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{9}\right)+\left(\frac{1}{9}-\frac{1}{13}\right)+...+\left(\frac{1}{2001}-\frac{1}{2005}\right)\)

\(=1+\left(-\frac{1}{5}+\frac{1}{5}\right)+\left(-\frac{1}{9}+\frac{1}{9}\right)+...+\left(-\frac{1}{2001}+\frac{1}{2001}\right)-\frac{1}{2005}\)

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

\(=\frac{2004}{2005}\)

2/5 . A = 2/10.12 + 2/12.14 + ....... + 2/998.1000

           = 1/10 - 1/12 + 1/12 - 1/14 + ..... + 1/998 - 1/1000

           = 1/10 - 1/1000 = 99/1000

=> A = 99/1000 : 2/5 = 99/400

Tk mk nha

Mình làm tắt cũng dc nhé có gì ko dc hỏi mình nhé

Ta có:A=(5/10-5/12):2+(5/12-2/14):2+...+(5/998-5/1000):2

suy ra A=5/10-5/1000=99/200

`A=4/10.12+4/12.14+4/14.16+...+4/96.98`

`=2(2/10.12+2/12.14+2/14.16+...+2/96.98)`

`=2(1/10-1/12+1/12-1/14+1/14-1/16+...+1/96-1/98)`

`=2(1/10-1/98)`

`=2 . 22/245`

`=44/245`

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