Question

1/1×2 + 1/2×3 + 1/3×4 +......+ 1/99×100

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Answer 1

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)

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

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

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

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

Answer 2

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Answer 3

\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)

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

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

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