\(A=7\left(\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}+...+\dfrac{1}{69}-\dfrac{1}{70}\right)\)

\(=7\left(\dfrac{1}{10}-\dfrac{1}{70}\right)=\dfrac{7.60}{700}=\dfrac{420}{700}=\dfrac{3}{5}\)

\(B=\dfrac{1}{2}\left(\dfrac{1}{25}-\dfrac{1}{27}+\dfrac{1}{27}-\dfrac{1}{29}+...+\dfrac{1}{73}-\dfrac{1}{75}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{1}{25}-\dfrac{1}{75}\right)=\dfrac{1}{75}\)

Gọi \(\dfrac{1}{25.27}+\dfrac{1}{27.29}+\dfrac{1}{29.31}+...+\dfrac{1}{73.75}\)

là A, ta có

\(A=\dfrac{1}{25.27}+\dfrac{1}{27.29}+\dfrac{1}{29.31}+...+\dfrac{1}{73.75}\)

\(\Rightarrow2.A=\dfrac{2}{25.27}+\dfrac{2}{27.29}+\dfrac{2}{29.31}+...+\dfrac{2}{73.75}\)\(\Rightarrow2.A=\dfrac{1}{25}-\dfrac{1}{27}+\dfrac{1}{27}-\dfrac{1}{29}+...+\dfrac{1}{73}-\dfrac{1}{75}\)\(\Rightarrow2.A=\dfrac{1}{25}-\dfrac{1}{75}\)

\(\Rightarrow2.A=\dfrac{2}{75}\)

\(\Rightarrow A=\dfrac{2}{75}\div2\)

\(\Rightarrow A=\dfrac{1}{75}\)

KL: Vậy A =\(\dfrac{1}{75}\)

B=1/2. (2/25.27+2/27.29+2/29.31+....+2/73.75) B=1/2. (1/25-1/27+1/27-1/29+1/29-1/31+....+1/73-1/75) B=1/2. (1/25-1/75) B=1/2. 2/75 B=1/75

\(3A=\dfrac{3}{8.11}+\dfrac{3}{18.21}+..+\dfrac{3}{197.200}\)

xl bạn , mình gửi nhầm câu a =)

a, \(\frac{1}{25.27}+\frac{1}{27.29}+...+\frac{1}{73.75}\)

\(=\frac{1}{2}\left(\frac{2}{25.27}+\frac{2}{27.29}+...+\frac{2}{73.75}\right)\)

\(=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+...+\frac{1}{73}-\frac{1}{75}\right)\)

\(=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{75}\right)\)

\(=\frac{1}{2}\left(\frac{2}{75}\right)\)

\(=\frac{1}{75}\)

b, \(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)

\(=2\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2008.2010}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{2010}\right)\)

\(=2\left(\frac{1004}{2010}\right)\)

\(=2\left(\frac{502}{1005}\right)\)

\(=\frac{1004}{1005}\)

Tk hộ =v

\(\frac{1}{25.27}+\frac{1}{27.29}+\frac{1}{29.31}+...+\frac{1}{73.75}=\frac{1}{2}.\left(\frac{2}{25.27}+\frac{2}{27.29}+\frac{2}{29.31}+...+\frac{2}{73.75}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+\frac{1}{29}-\frac{1}{31}+...+\frac{1}{73}-\frac{1}{75}\right)=\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{75}\right)=\frac{1}{2}.\frac{2}{75}=\frac{1}{75}\)

\(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}=2.\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2008.2010}\right)\)

\(=2.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2008}-\frac{1}{2010}\right)=2.\left(\frac{1}{2}-\frac{1}{2010}\right)=2.\frac{502}{1005}=\frac{1004}{1005}\)

\(\frac{1}{25.27}+\frac{1}{27.29}+\frac{1}{29.31}+...+\frac{1}{73.75}\)

\(=\frac{1}{2}.\left(\frac{2}{25.27}+\frac{2}{27.29}+\frac{2}{29.31}+...+\frac{2}{73.75}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+\frac{1}{29}-\frac{1}{31}+...+\frac{1}{73}-\frac{1}{75}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{75}\right)\)

\(=\frac{1}{2}.\left(\frac{3}{75}-\frac{1}{75}\right)\)

\(=\frac{1}{2}.\frac{2}{75}\)

\(=\frac{1}{75}\)

Câu dưới đặt 2 ra ngoài rồi làm bình thường.

\(\Rightarrow2A=\frac{2}{25.27}+\frac{2}{27.29}+\frac{2}{29.31}+...+\frac{2}{73.75}\)

\(\Rightarrow2A=\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{31}+...+\frac{1}{73}-\frac{1}{75}\)

\(\Rightarrow2A=\frac{1}{25}-\frac{1}{75}=\frac{3}{75}-\frac{1}{75}=\frac{2}{75}\)

\(\Rightarrow A=\frac{2}{75}\div2=\frac{1}{75}\)

1) A=7/10.11+7/11.12+7/12.13+...+7/69.70

  A=7.(1/10.11+1/11.12+1/12.13+...+1/69.70)

 A= 7.(1/10-1/11+1/11-1/12+1/12-1/13+...+1/69-1/70)

 A= 7.(1/10-1/70)

 A=7.3/35=3/5

2)B=1/25.27+1/27.29+1/29.31+...+1/73.1/75

  B=1/25-1/27+1/27-1/29+1/29-1/31+...+1/73-1/75

  B=1/25-1/75=2/75

A = 7/ 10.11 + 7/ 11.12 + 7/ 12.13 + .... + 7/69.70

(1/7).A=1/10.11+1/11.12+...+1/69.70

=1/10-1/11+1/11-1/12+...+1/69-1/70

=1/10-1/70=3/35

=>A=7.(3/35)

=3/5

2 ) B = 1/ 25.27 + 1/ 27.29 + 1/29.31+ ......+ 1/ 73.75

=>(1/2).B=2/25.27+...+2.73.75

=1/25-1/27+...+1/73-1/75

=1/25-1/75

=2/75

=>B=4/75

 A=7.(1/10.11+1/11.12+1/12.13+...+1/69.70)

 A= 7.(1/10-1/11+1/11-1/12+1/12-1/13+...+1/69-1/70)

 A= 7.(1/10-1/70)

 A=7.3/35=3/5

2)B=1/25.27+1/27.29+1/29.31+...+1/73.1/75

  B=1/25-1/27+1/27-1/29+1/29-1/31+...+1/73-1/75

  B=1/25-1/75=2/75

Ta có :

\(B=\frac{1}{25.27}+\frac{1}{27.29}+\frac{1}{29.31}+...+\frac{1}{73.75}\)

\(2B=\frac{2}{25.27}+\frac{1}{27.29}+\frac{2}{29.31}+...+\frac{2}{73.75}\)

\(2B=\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+....+\frac{1}{73}-\frac{1}{75}\)

\(2B=\frac{1}{25}-\frac{1}{75}\)

\(2B=\frac{2}{75}\)

\(\Rightarrow B=\frac{1}{75}\)

Vậy B = \(\frac{1}{75}\)

\(F=\frac{4}{2.3}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)

\(\Rightarrow F=2\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{2008.2010}\right)\)

\(\Rightarrow F=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)

\(\Rightarrow F=2\left(\frac{1}{2}-\frac{1}{2010}\right)\)

\(\Rightarrow F=2.\frac{502}{1005}=\frac{1004}{1005}\)

Vậy F = \(\frac{1004}{1005}\)