Question

tinh gia tri bieu thuc a = \(\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{99\times100}\)

Answer 1

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.......+\frac{1}{99}-\frac{1}{100}\)

\(=1-\frac{1}{100}=\frac{99}{100}\)

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Answer 2

\(a=\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{99\times100}\)

\(a=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)

\(a=1-\frac{1}{100}\)

\(a=\frac{99}{100}\)