Question

Tính tổng :

A=\(\frac{1}{1×2}+\frac{1}{2×3}+\frac{1}{3×4}+.....+\frac{1}{999.1000}\)

Answer 1

\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{999}-\frac{1}{1000}\)\

\(A=1-\frac{1}{1000}=\frac{999}{1000}\)

Answer 2

A=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{999.1000}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{999}-\frac{1}{1000}\)

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

\(A=\frac{999}{1000}\)

Answer 3

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{999}-\frac{1}{1000}\)

\(A=1-\frac{1}{1000}=\frac{999}{1000}\)

Answer 4

\(A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{999\cdot1000}\)

  \(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{999}-\frac{1}{1000}\)

   \(=1-\frac{1}{1000}\)

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

    \(=\frac{999}{1000}\)

Answer 5

A=1-1/1000