Question

Cho A= \(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{2016}+\frac{1}{2017}\)

         

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

Tinh \(\frac{B}{A}\)giai ra giup minh voi

Answer 1

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

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

\(B=1+\left(\frac{2015}{2}+1\right)+...+\left(\frac{2}{2015}+1\right)+\left(\frac{1}{2016}+1\right)\)

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

\(B=2017\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2016}+\frac{1}{2017}\right)\)

\(\frac{B}{A}=\frac{2017\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2016}+\frac{1}{2017}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2016}+\frac{2}{2017}}=2017\)