Question

1/99.100-1/98.99-1/97.98-....-1/15.16

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Answer 1

\(\frac{1}{99.100}-\frac{1}{98.99}-\frac{1}{97.98}-...-\frac{1}{15.16}\)

\(=\frac{1}{99.100}-\left(\frac{1}{15.16}+\frac{1}{16.17}+...+\frac{1}{97.98}+\frac{1}{98.99}\right)\)

\(=\frac{1}{9900}-\left(\frac{1}{15}-\frac{1}{16}+\frac{1}{16}-\frac{1}{17}+...+\frac{1}{97}-\frac{1}{98}+\frac{1}{98}-\frac{1}{99}\right)\)

\(=\frac{1}{9900}-\left(\frac{1}{15}-\frac{1}{99}\right)\)

\(=\frac{1}{9900}-\frac{28}{495}=-\frac{559}{9900}\)

Answer 2

=\(\frac{559}{9900}\)

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