Question

Tính \(\frac{A}{B}\)biết 

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

\(B=\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}\)

 

Answer 1

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

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

\(A=\frac{2011}{2011}+\frac{2011}{2}+...+\frac{2011}{2009}+\frac{2011}{2010}\)

\(A=\frac{2011}{2}+...+\frac{2011}{9}+\frac{2011}{10}+\frac{2011}{11}\)

\(A=2011.\left(\frac{1}{2}+...+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}\right)\)

\(A=2011.B\)

Nên : \(\frac{A}{B}=\frac{2011.B}{B}=2011\)

Vậy \(\frac{A}{B}=2011\)

Tham khảo nha !!! Chúc bạn học tốt !!!