Question

Thực hiện phép tính:

\(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\)

Giúp mik với ạ

Answer 1

Ta có: \(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\)

\(=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)

\(=2\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{240}\right)\)

\(=2\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{15.16}\right)\)

\(=2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\right)\)

\(=2\left(\frac{1}{4}-\frac{1}{16}\right)\)

\(=2.\frac{3}{16}=\frac{3}{8}\)

Answer 2

\(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\)

\(=\frac{2}{20}+\frac{2}{\text{​​}30}+\frac{2}{42}+...+\frac{2}{240}\)

\(=2\cdot\left(\frac{1}{20}+\frac{1}{\text{​​}30}+\frac{1}{42}+...+\frac{1}{240}\right)\)

\(=2\cdot\left(\frac{1}{4\cdot5}+\frac{1}{\text{​​}5\cdot6}+\frac{1}{6\cdot7}+...+\frac{1}{15\cdot16}\right)\)

\(=2\cdot\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{\text{​​}5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\right)\)

\(=2\cdot\left(\frac{1}{4}-\frac{1}{16}\right)\)

\(=2\cdot\left(\frac{4}{16}-\frac{1}{16}\right)\)

\(=2\cdot\frac{3}{16}\)

\(=\frac{3}{8}\)