Question

Thực hiện phép tính:

\(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2016}+\frac{1}{2017}}{\frac{2016}{1}+\frac{2015}{2}+\frac{2014}{3}+...+\frac{2}{2015}+\frac{1}{2016}}\)

Answer 1

Answer 2

Đặt B= \(\dfrac{2016}{1}\)+ \(\dfrac{2015}{2}\)+...+ \(\dfrac{2}{2015}\)+\(\dfrac{1}{2016}\)

= \(\dfrac{2016}{1}\)+1+\(\dfrac{2015}{2}\)+1+...+\(\dfrac{2}{2015}\)+1+\(\dfrac{1}{2016}\)+1- 2016

= \(\dfrac{2017}{2}\)+...+\(\dfrac{2017}{2015}\)+\(\dfrac{2017}{2016}\)+2017 -2016

= \(\dfrac{2017}{2}\)+...+\(\dfrac{2017}{2015}\)+\(\dfrac{2017}{2016}\)+\(\dfrac{2017}{2017}\)

= 2017. (\(\dfrac{1}{2}\)+\(\dfrac{1}{3}\)+...+\(\dfrac{1}{2016}\)+\(\dfrac{1}{2017}\))

=> phép tính = \(\dfrac{1}{2017}\)