Question

1/2*3+1/3*4+.....+1/99+100

Answer 1

Sửa đề :\(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{99\cdot100}\)

\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\)

\(=\dfrac{1}{2}-\dfrac{1}{100}\)

\(=\dfrac{50}{100}-\dfrac{1}{100}\)

`= 49/100`

Answer 2

 Sửa đề:\(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\)
\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\)
\(=\dfrac{1}{2}-\dfrac{1}{100}\)
\(=\dfrac{50}{100}-\dfrac{1}{100}\)
\(=\dfrac{49}{100}\)

Answer 3