Question

\(\dfrac{\text{3}}{\text{2}}+\dfrac{\text{7}}{\text{6}}+\dfrac{\text{13}}{12}+\dfrac{\text{21}}{\text{20}}+\dfrac{\text{31}}{\text{30}}+\dfrac{\text{43}}{\text{42}}+\dfrac{\text{57}}{\text{56}}\)
Tính nhanh: lời giải chi tiết

Answer 1

`3/2 + 7/6 + 13/12 + 21/20 + 31/30 + 43/42 + 57/56`

`= 1 + 1/2 + 1 + 1/6 + 1 + 1/12 + 1 + 1/20 + 1 + 1/30 + 1 + 1/42 + 1 + 1/56`

`=(1+1+1+1+1+1)+(1/2+1/6+1/12+1/20+1/30 + 1/42 + 1/56)`

\(=6+\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}\right)\)

`=6 + (1-1/2+1/2-1/3+.......+1/7-1/8)`

`=6 + (1 - 1/8)`

`=6 + (8/8-1/8)`

`=6 + 7/8`

`=48/8 + 7/8`

`=(48+7)/8`

`=55/8`

Answer 2

\(=1+\dfrac{1}{2}+1+\dfrac{1}{6}+1+\dfrac{1}{12}+1+\dfrac{1}{20}+1+\dfrac{1}{42}+1+\dfrac{1}{56}\)

=6+1-1/2+1/2-1/3+...+1/7-1/8

=6+7/8

=55/8