Question

 

giúp mình với mik đang cần ngay

5/4.6 + 5/6.8 + 5/8.10 + ..........+5/198.200

Answer 1

\(\frac{5}{4.6}+\frac{5}{6.8}+\frac{5}{8.10}+...+\frac{5}{198.200}\)

\(=\frac{5}{2}\left(\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+...+\frac{2}{198.200}\right)\)

\(=\frac{5}{2}\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\right)\)

\(=\frac{5}{2}\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\right)\)

\(=\frac{5}{2}\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(=\frac{5}{2}\left(\frac{50}{100}-\frac{1}{100}\right)\)

\(=\frac{5}{2}.\frac{49}{100}\)

\(=\frac{49}{40}\)

Answer 2

Ta sẽ tách 5 ra ngoài

Answer 3

Bạn Vũ Đình phước ơi sao bạn ko tách số 5 ở tử rồi nhân thêm 5 ở phân số.

Answer 4

 đặt A = \(\frac{5}{4.6}+\frac{5}{6.8}+\frac{5}{8.10}+....+\frac{5}{198.200}\)

\(A=5\left(\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+...+\frac{1}{198.200}\right)\)

\(\Rightarrow2A=5\left(\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+...+\frac{2}{198.200}\right)\)

\(\Rightarrow2A=5\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+...+\frac{1}{198}-\frac{1}{200}\right)\)

\(\Rightarrow2A=5\left(\frac{1}{4}-\frac{1}{200}\right)\)

\(\Rightarrow2A=5\cdot\frac{49}{200}\)

\(\Rightarrow2A=\frac{49}{40}\)

\(\Rightarrow A=\frac{49}{40}:2\) 

\(\Rightarrow A=\frac{49}{80}\)