Question

Cho mik hỏi : 2/99-2/99.97-2/97.95-...-2/5.3-2/3.1

Answer 1

\(\frac{2}{99}-\frac{2}{99.97}-\frac{2}{97.95}-...-\frac{2}{5.3}-\frac{2}{3.1}\)

= \(\frac{2}{99}-\left(\frac{2}{99.97}+\frac{2}{97.95}+...+\frac{2}{5.3}+\frac{2}{3.1}\right)\)

= \(\frac{2}{99}-\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{95.97}+\frac{2}{97.99}\right)\)

= \(\frac{2}{99}-\left(\frac{2}{1}-\frac{2}{3}+\frac{2}{3}-\frac{2}{5}+...+\frac{2}{95}-\frac{2}{97}+\frac{2}{97}-\frac{2}{99}\right)\)

= \(\frac{2}{99}-\left(2-\frac{2}{99}\right)\) = \(\frac{2}{99}-\left(\frac{198}{99}-\frac{2}{99}\right)\) = \(\frac{2}{99}-\frac{198}{99}+\frac{2}{99}\) = \(-\frac{194}{99}\)

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