Question

\(\frac{2010}{1}+\frac{2009}{2}+\frac{2008}{3}+.....+\frac{1}{2010}\)
 

\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+......+\frac{1}{2011}\)

Tính 

Answer 1

\(\frac{2010}{1}+\frac{2009}{2}+...+\frac{1}{2010}\)

\(=\left(1+1+...+1\right)+\frac{2009}{2}+...+\frac{1}{2010}\)

\(=\left(\frac{2009}{2}+1\right)+\left(\frac{2008}{3}+1\right)+...+\left(\frac{1}{2010}+1\right)+1\)

\(=\frac{2011}{2}+\frac{2011}{3}+...+\frac{2011}{2010}+\frac{2011}{2011}\)

\(=2011.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2010}+\frac{1}{2011}\right)\)

Ta thấy tử số gấp 2011 lần mẫu số nên phép tính này=2011