Question

Tính 

5/15.16+5/16.17+5/17.18+5/18.19+5/19.20

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Answer 1

5/15.16+5/16.17+5/17.18+5/18.19+5/19.20

=5(1/15-1/16+1/16-1/17+..+1/19-1/20) 

=5.(1/15-1/20)

=5.1/60

=1/12

Answer 2

\(\frac{5}{15.16}+\frac{5}{16.17}+\frac{5}{17.18}+\frac{5}{18.19}+\frac{5}{19.20}\)

= \(5.\left(\frac{1}{15.16}+\frac{1}{16.17}+\frac{1}{17.18}+\frac{1}{18.19}+\frac{1}{19.20}\right)\)

= \(5.\left(\frac{1}{15}-\frac{1}{16}+\frac{1}{16}-\frac{1}{17}+\frac{1}{17}-\frac{1}{18}+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\right)\)

= \(5.\left(\frac{1}{15}-\frac{1}{20}\right)\)

= \(5.\frac{1}{60}\)

= \(\frac{1}{12}\)

Answer 3

\(\frac{5}{15.16}+\frac{5}{16.17}+\frac{5}{17.18}+\frac{5}{18.19}+\frac{5}{19.20}\)

\(=5\left(\frac{1}{15.16}+\frac{1}{16.17}+...+\frac{1}{19.20}\right)\)

\(=5\left(\frac{1}{15}-\frac{1}{16}+\frac{1}{16}-\frac{1}{17}+...+\frac{1}{19}-\frac{1}{20}\right)\)

\(=5\left(\frac{1}{15}-\frac{1}{20}\right)\)

\(=5.\frac{1}{60}\)

\(=\frac{1}{12}\)