Question

\(\frac{1}{2}+\frac{1}{14}+\frac{1}{35}+\frac{1}{65}+.....+\frac{1}{4850}\)

                tính nha

Answer 1

\(\frac{1}{2}+\frac{1}{14}+\frac{1}{35}+\frac{1}{65}+...+\frac{1}{4850}\)

\(=\frac{2}{4}+\frac{2}{28}+\frac{2}{70}+\frac{2}{130}+...+\frac{2}{9700}\)

\(=2.\left(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+...+\frac{1}{97.100}\right)\)

\(=\frac{2}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{97.100}\right)\)

\(=\frac{2}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{97}-\frac{1}{100}\right)\)

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

\(=\frac{2}{3}.\frac{99}{100}=\frac{33}{50}\)

Answer 2

sao lại có 2/3 ở đây