Question

Tính tổng :

\(\dfrac{5}{1.3}\)+\(\dfrac{5}{3.5}\)+....+\(\dfrac{5}{99.101}\)

Answer 1

`5/(1.3)+5/(3.5)+....+5/(99.101)`

`=5/2(2/(1.3)+2/(3.5)+....+2/(99.101))`

`=5/2(1-1/3+1/3-1/5+...+1/99-1/101)`

`=5/2(1-1/101)`

`=5/2*100/101`

`=250/101`

Answer 2

Ta có: \(\dfrac{5}{1\cdot3}+\dfrac{5}{3\cdot5}+...+\dfrac{5}{99\cdot101}\)

\(=\dfrac{5}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{99\cdot101}\right)\)

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

\(=\dfrac{5}{2}\cdot\dfrac{100}{101}\)

\(=\dfrac{250}{101}\)