Question

Tính nhanh:

1/42 + 1/56 + 1/72 + .... + 1/9900

Answer 1

`1/42 + 1/56 + 1/72 + .... + 1/9900`

`= 1/( 6*7) + 1/( 7*8 ) + ..... + 1/( 99*100)`

`= 1/6 - 1/7 + 1/7-1/8+....+1/99-1/100`

`= 1/6 - 1/100`

`= 50/300 - 3/300`

`= 47/300` 

Answer 2

\(\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+...+\dfrac{1}{9900}\\ =\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+...+\dfrac{1}{99.100}\\ =\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+...+\dfrac{1}{99}-\dfrac{1}{100}\\ =\dfrac{1}{6}-\dfrac{1}{100}=\dfrac{47}{300}\)