Question

Tính

\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+.....+\frac{2}{99.100}\)

Answer 1

\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+......+\frac{2}{99.100}\)

\(=2.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{99.100}\right)\)

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

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

\(=2.\frac{99}{100}=\frac{99}{50}\)

Answer 2

=\(2\left(\frac{1}{1.2}+\frac{1}{2.3}+..+\frac{1}{99.100}\right)\)

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

=\(2\cdot\frac{99}{100}=\frac{99}{50}\)

Answer 3

=2(1/1.2+1/2.3+1/3.4+...+1/99.100)

=2(1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100)

=2(1-1/100)

=2.99/100=99/50

Answer 4

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