Question

[nguyendinhhoa]

C= 1/10+1/15+1/21+..............+1/120

các số trên đều là phân số

Answer 1

[Kaito]

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

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

\(C=\frac{2}{4\times5}+\frac{2}{5\times6}+\frac{2}{6\times7}+...+\frac{2}{15\times16}\)

\(C=2\times\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)\)

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

\(C=2\times\frac{3}{16}=\frac{3}{8}\)

Answer 2

[Nguyễn Hưng Phát]

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

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

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

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

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

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