Question

A=\(\frac{1}{2.4}\)+\(\frac{1}{4.6}\)+\(\frac{1}{6.8}\)+.....+\(\frac{1}{98.100}\)

Ai giải được mik tick cho nha

Answer 1

Ta có:

\(A=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{98.100}\)

\(\Rightarrow A=\frac{1}{2}.\left(\frac{2}{2.4}+\frac{1}{4,6}+\frac{1}{6.8}+...+\frac{1}{98.100}\right)\)

\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}\right)\)

\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(\Rightarrow A=\frac{1}{2}.\frac{49}{100}=\frac{49}{200}\)

Answer 2

Đặt \(A=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{98.100}\)

\(4-2=2;6-4=2;...\)

\(2A=\frac{1}{2}-\left(\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}\right)\)

\(2A=\frac{1}{2}-\frac{1}{100}\)

\(2A=\frac{49}{100}\)

Answer 3

\(\frac{1}{2}\)lấy đâu ra

Answer 4

Đơn giản thôi: 

Phân tích: \(\frac{1}{2.4}=\frac{1}{2}-\frac{1}{4};...\)

Từ đó ta có phân số \(\frac{1}{2}\)

Answer 5

thầy giáo tớ bảo là \(\frac{49}{100}\) là sai

Answer 6

Ta có :

A=1/2.4+1/4.6+...+1/98.100

=> A=1.2/2.4.2+1.2/4.6.2+...+1.2/98.100.2

=> A=1/2.(2/2.4+2/4.6+...+2/98.100)

=> A=1/2.(1-1/4+1/4-1/6+...+1/98-1/100)

=> A=1/2.(1-1/100)

=> A=1/2.99/100

=> A=99/200

Vậy A=99/200

Answer 7

\(A=\frac{1}{2\cdot4}+\frac{1}{4\cdot6}+\frac{1}{6\cdot8}+...+\frac{1}{98\cdot100}\)

=>\(2A=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+....+\frac{2}{98\cdot100}\)

         \(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}\)

         \(=\frac{1}{2}-\frac{1}{100}\)

         \(=\frac{50}{100}-\frac{1}{100}\)

          \(=\frac{49}{100}\)

Answer 8

\(A=\frac{1}{2\cdot4}+\frac{1}{4\cdot6}+\frac{1}{6\cdot8}+...+\frac{1}{98\cdot100}\)

=>\(2A=\frac{2}{2\cdot4}+\frac{2}{4\cdot6}+\frac{2}{6\cdot8}+...+\frac{2}{98\cdot100}\)

          \(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}\)

           \(=\frac{1}{2}-\frac{1}{100}\)

          \(=\frac{50}{100}-\frac{1}{100}\)

           \(=\frac{49}{100}\)

=>   A= 2A : 2

=>    \(A=\frac{49}{100}:2\)

             \(=\frac{49}{100}\cdot\frac{1}{2}\)

            \(=\frac{49}{200}\)

Answer 9

\(A=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{98.100}\)

\(2A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}\)

\(2A=\frac{1}{2}-\frac{1}{100}\)

\(2A=\frac{49}{100}\)

\(A=\frac{49}{100}:2\)

\(A=\frac{49.1}{100.2}=\frac{49}{200}\)

Answer 10

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