Question

\(\frac{1}{3x5}+\frac{1}{5x7}+....+\frac{1}{99.101}\)

\(5!=?\)

Answer 1

\(=\frac{98}{303}\)

\(5!=1.2.3.4.5=120\)

Answer 2

120 nha bạn

Answer 3

\(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{99.101}=\frac{1}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\right)\)

\(=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{101}\right)=\frac{1}{2}.\frac{98}{303}=\frac{49}{303}\)

5!=1.2.3.4.5=(2.5).(3.4)=10.12=120

Chúc bạn học giỏi !