Question

Hãy tính cho mình bài này:

\(\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+...+\frac{2}{99.100}\)\(\)

[Nhớ trình bày phép tính]

Answer 1

\(\frac{2}{2\cdot3}+\frac{2}{3\cdot4}+\frac{2}{4\cdot5}+...+\frac{2}{99\cdot100}\)

\(=2\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{99\cdot100}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(=2\cdot\frac{49}{100}\)

\(=\frac{49}{50}\)

Answer 2

=2(\(\frac{1}{2.3}\)+\(\frac{1}{3.4}\)+\(\frac{1}{4.5}\)+...+\(\frac{1}{99.100}\))

=2(\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+...+\(\frac{1}{99}\)-\(\frac{1}{100}\))

=2(\(\frac{1}{2}\)-\(\frac{1}{100}\))

=2.\(\frac{49}{100}\)

=\(\frac{49}{50}\)