Question

[Lê Khánh Lâm]

6/4*7 + 6/7*10 + 6/10*13 +... + 6/97*100

Answer 1

[Thu Huệ]

\(\frac{6}{4\cdot7}+\frac{6}{7\cdot10}+\frac{6}{10\cdot13}+...+\frac{6}{97\cdot100}\)

\(=2\left(\frac{3}{4\cdot7}+\frac{3}{7\cdot10}+\frac{3}{10\cdot13}+...+\frac{3}{97\cdot100}\right)\)

\(=2\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{97}-\frac{1}{100}\right)\)

\(=2\left(\frac{1}{4}-\frac{1}{100}\right)\)

\(=2\cdot\frac{24}{100}=\frac{24}{50}=\frac{12}{25}\)

Answer 2

[Huỳnh Quang Sang]

Đặt \(A=\frac{6}{4\cdot7}+\frac{6}{7\cdot10}+\frac{6}{10\cdot13}+...+\frac{6}{97\cdot100}\)

\(A=\)\(2\cdot\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{97}-\frac{1}{100}\right)\)

\(A=2\left(\frac{1}{4}-\frac{1}{100}\right)\)

\(A=2\left(\frac{25}{100}-\frac{1}{100}\right)\)

\(A=2\cdot\frac{24}{100}=2\cdot\frac{6}{25}=\frac{12}{25}\)