a,ta thay hai so o duoi mau so la hai sop tu nhien lien tiep khoang cach chinh bang 1 

ta co 1/3-1/4+1/4-1/5+.............................+1/20-1/21

ta co =1/3-1/21 vi co cac so doi to da the hien tren 

=2/7

b vi khoang cach duoi mau kac tu mau la 2 con tu la 1 vay nhan 2 vao ca day so ta duoc 

2/4.6+2/6.8+..............................+2/30.32

bay gio khoang cach duoi mau bang tu ta co

1/4-1/6+1/6-1/8+............................+1/30-1/32

nhu tren ta co =(1/4-1/32):2=7/64

=3(1/2 -1/34)=3(17-1)/34=3.16/34=24/17

Đs: 24/17

dễ

bằng 24/17

k cho mình nha

Đáp số:24/17

Gọi tổng cần tính là \(A\)

Ta có: \(A=\dfrac{1}{2.4}+\dfrac{1}{4.6}+\dfrac{1}{6.8}+...+\dfrac{1}{38.40}\)

\(\Rightarrow2A=\dfrac{2}{2.4}+\dfrac{2}{4.6}+\dfrac{2}{6.8}+...+\dfrac{2}{38.40}\)

\(\Rightarrow2A=\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+...+\dfrac{1}{38}-\dfrac{1}{40}\)

\(\Rightarrow2A=\dfrac{1}{2}-\dfrac{1}{40}=\dfrac{19}{40}\)

\(\Rightarrow A=\dfrac{\dfrac{19}{40}}{2}=\dfrac{19}{80}\)

A=1/2.4+1/4.6+........+1/100.102

A=1/2-1/4+1/4-1/6+.......+1/100-1/102

A=1/2-1/102

A=51/102-1/102

A=50/102

A=25/51

\(A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-...+\frac{1}{18}-\frac{1}{20}\)

\(A=\frac{1}{2}-\frac{1}{20}\)

\(A=\frac{10}{20}-\frac{1}{20}\)

\(A=\frac{9}{20}\)

\(A=\dfrac{6}{2.4}+\dfrac{6}{4.6}+\dfrac{6}{6.8}+\dfrac{6}{8.10}+...+\dfrac{6}{30.32}+\dfrac{6}{32.34}\)

\(=6\left(\dfrac{1}{2.4}+\dfrac{1}{4.6}+\dfrac{1}{6.8}+\dfrac{1}{8.10}+...+\dfrac{1}{30.32}+\dfrac{1}{32.34}\right)\)

\(=6\cdot\dfrac{2}{2}\left(\dfrac{1}{2.4}+\dfrac{1}{4.6}+\dfrac{1}{6.8}+\dfrac{1}{8.10}+...+\dfrac{1}{30.32}+\dfrac{1}{32.34}\right)\)

\(=\dfrac{6}{2}\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+\dfrac{2}{6.8}+\dfrac{2}{8.10}+...+\dfrac{2}{30.32}+\dfrac{2}{32.34}\right)\)

\(=3\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{10}+...+\dfrac{1}{30}-\dfrac{1}{32}+\dfrac{1}{32}-\dfrac{1}{34}\right)\)

\(=3\left(\dfrac{1}{2}-\dfrac{1}{34}\right)=3\cdot\dfrac{8}{17}=\dfrac{24}{17}\)

A\(=6\left(\dfrac{1}{2.4}+\dfrac{1}{4.6}+\dfrac{1}{6.8}+...+\dfrac{1}{32.34}\right)\)

A\(=6.\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{32}-\dfrac{1}{34}\right)\)

A\(=3\left(\dfrac{1}{2}-\dfrac{1}{34}\right)\)

A\(=3.\dfrac{8}{17}\)

A\(=\dfrac{24}{17}\)

\(S=\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{2018.2020}\)

\(S=\frac{1}{2}\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{2018.2020}\right)\)

\(S=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2018}-\frac{1}{2020}\right)\)

\(S=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{2020}\right)\)

Tự tính

S=1/2.4+1/4.6+1/6.8+...+1/2018.2020

S=1/2.(2/2.4+2/4.6+2/6.8+...+2/2018.2020)

S=1/2.(1-1/4+1/4-1/6+1/6-1/8+...+1/2018-1/2020)
S=1/2.(1-1/2020)

S=1/2.(2020/2020-1/2020)

S=1/2.2019/2020

S=2019/4040

\(S=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2018}-\frac{1}{2020}\right)\)

\(S=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{2020}\right)\)

\(S=\frac{1}{4}-\frac{1}{4040}=\frac{1010}{4040}-\frac{1}{4040}=\frac{1009}{4040}\)

\(S=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}\)

\(S=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}\)

\(S=\frac{1}{2}-\frac{1}{10}\)

\(S=\frac{2}{5}\)

S = 1 / 2.4 + 1/ 4.6 + 1 / 6.8 + 1 / 8.10

2S = 2 / 2.4 + 2 / 4.6 + 2/ 6.8 + 2 / 8.10

2S = 1 2 - 1 / 4 + 1 / 4 - 1 / 6 + 1 / 6 - 1 / 8 + 1 / 8 - 1 / 10

2S = 1 / 2 - 1 / 10

2S = 2 / 5 

  S = 2 / 5 : 2

  S = 1 / 5