Question

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

Answer 1

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

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

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

\(S=\frac{2.99}{100}=\frac{99}{50}=1,98\)

Answer 2

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

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

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

\(2S=\frac{99}{100}\)

\(S=\frac{99}{100}:2\)

\(S=\frac{99}{200}\)

Answer 3

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

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

\(S=2\left(1-\frac{1}{100}\right)=2.\frac{99}{100}=\frac{99}{50}=1.98\)

Answer 4

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

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

\(\frac{1}{2}S=\frac{99}{100}\)

\(S=\left(\frac{99}{100}\right)\div2\) nha bạn

Answer 5

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

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

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

\(S=\frac{99}{100}\div\frac{1}{2}\)

\(S=\frac{99}{50}\)