Question

Tính nhanh

A = \(\frac{1}{1.5}+\frac{1}{5.10}+\frac{1}{10.15}+...+\frac{1}{90.95}+\frac{1}{95.100}\)

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Answer 1

\(A=\frac{1}{1.5}+\frac{1}{5.10}+\frac{1}{10.15}+...+\frac{1}{95.100}\)

\(\Rightarrow\)\(5A=1+\frac{5}{5.10}+\frac{5}{10.15}+...+\frac{5}{95.100}\)

               \(=1+\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+...+\frac{1}{95}-\frac{1}{100}\)

              \(=1+\frac{1}{5}-\frac{1}{100}=\frac{119}{100}\)

\(\Rightarrow\)\(A=\frac{119}{500}\)

Answer 2

A=1/1.5+1/5.10+....+1/95.100

=(5/1.5+5/5.10+...+5/95.100):5

=(1-1/5+1/5-1/10+...+1/95-1/100):5

=(1-1/100):5

=99/100:5

=99/500

Answer 3

A=1-1/5+1/5-1/10+...+1/95-1/100

A=1-1/100=99/100

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Answer 4

\(A=\frac{1}{1\cdot5}+\frac{1}{5\cdot10}+\frac{1}{10\cdot15}+....+\frac{1}{90\cdot95}+\frac{1}{95\cdot100}\)

\(A=\frac{1}{5}\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{10}+...+\frac{1}{95}-\frac{1}{100}\right)\)

\(A=\frac{1}{5}\left(1-\frac{1}{100}\right)\)

\(A=\frac{1}{5}\cdot\frac{99}{100}\)

\(A=\frac{99}{500}\)

Vậy ......

Answer 5

\(A=\frac{1}{5}+\frac{1}{5}\left(\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+...+\frac{1}{95}-\frac{1}{100}\right)\)

\(=\frac{1}{5}+\frac{1}{5}\left(\frac{1}{5}-\frac{1}{100}\right)\)

\(=\frac{1}{5}+\frac{1}{5}.\frac{19}{100}\)

\(=\frac{119}{500}\)

Answer 6

\(A=\frac{1}{1.5}+\frac{1}{5.10}+...+\frac{1}{95.100}\)

     \(=\frac{1}{5}+\frac{1}{5}\left(\frac{5}{5.10}+\frac{5}{10.15}+...+\frac{5}{95.100}\right)\)

      \(=\frac{1}{5}+\frac{1}{5}\left(1-\frac{1}{10}+...+\frac{1}{95}-\frac{1}{100}\right)\)

       \(=\frac{1}{5}+\frac{1}{5}\left(1-\frac{1}{100}\right)\)

        \(=\frac{1}{5}+\frac{1}{5}.\frac{99}{100}\)

          \(=\frac{1}{5}\left(1+\frac{99}{100}\right)\)

        \(=\frac{1}{5}.\frac{199}{100}=\frac{199}{500}\)