Question

Tính tổng các phân số sau:

\(A=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{24.25}\)

Answer 1

\(A=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{24}-\frac{1}{25}\)\(\frac{1}{25}\)

\(A=\frac{1}{5}-\frac{1}{25}\)

\(A=\frac{5}{25}-\frac{1}{25}=\frac{4}{25}\)

Answer 2

\(A=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{24.25}\)

\(A=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{24}-\frac{1}{25}\)

\(A=\frac{1}{5}-\frac{1}{25}\)

\(A=\frac{4}{25}\)

Answer 3

\(A=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+.......+\frac{1}{24}-\frac{1}{25}\)

\(A=\frac{1}{5}+\left(-\frac{1}{6}+\frac{1}{6}\right)+\left(-\frac{1}{7}+\frac{1}{7}\right)+\left(-\frac{1}{8}+\frac{1}{8}\right)+.......+\left(-\frac{1}{24}+\frac{1}{24}\right)-\frac{1}{25}\)       

\(A=\frac{1}{5}-\frac{1}{25}=\frac{4}{25}\)