Question

A = \(\frac{1}{5.10}\)+ \(\frac{1}{10.15}\)+ \(\frac{1}{15.20}\)+ ...... + \(\frac{1}{995.1000}\)

Answer 1

\(A=\frac{1}{5}x\left(\frac{1}{5}+\frac{1}{10}+\frac{1}{10}+\frac{1}{995.1000}\right)\)

\(A=\frac{1}{5}x\left(\frac{1}{5}-\frac{1}{1000}\right)\)

\(A=\frac{1}{5}x\frac{199}{1000}\)

\(A=\frac{199}{5000}\)

Nếu muốn thì thử lại :

Answer 2

\(=\frac{1}{5}\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{10}+..+\frac{1}{995}-\frac{1}{1000}\right)...\)

\(=\frac{1}{5}\left(1-\frac{1}{1000}\right)=\frac{1}{5}\cdot\frac{995}{1000}\)

tự tính nốt nha

Answer 3

\(A=\frac{1}{5.10}+\frac{1}{10.15}+\frac{1}{15.20}+...+\frac{1}{995.1000}\)

\(5A=\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+\frac{1}{5}-\frac{1}{20}+...+\frac{1}{995}-\frac{1}{1000}\)

\(5A=\frac{1}{5}-\frac{1}{1000}\)

\(5A=\frac{199}{1000}\)

\(A=\frac{199}{1000}:5\)

\(A=\frac{199}{5000}\)

Answer 4

\(A=\frac{1}{5}.\left(\frac{1}{5}-\frac{1}{10} +\frac{1}{10}-\frac{1}{15}+...+\frac{1}{995}-\frac{1}{1000}\right)\)

\(A=\frac{1}{5}.\left(\frac{1}{5}-\frac{1}{1000}\right)\)

\(A=\frac{1}{5}.\frac{199}{1000}\)

\(A=\frac{199}{5000}\)