Question

Answer 1

\(A=\dfrac{2}{1}\cdot\dfrac{2}{3}\cdot\dfrac{3}{2}\cdot\dfrac{3}{4}\cdot...\cdot\dfrac{20}{19}\cdot\dfrac{20}{21}\)

\(=\dfrac{2}{1}\cdot\dfrac{3}{2}\cdot...\cdot\dfrac{20}{19}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot...\cdot\dfrac{20}{21}\)

=20/1*2/21=40/21

Answer 2

\(Q=1+\dfrac{1}{2}-\dfrac{1}{2}-\dfrac{1}{3}+....-\dfrac{1}{1010}-\dfrac{1}{1011}\)

=1-1/1011=1010/1011

 

A>1

Q<1

=>A>Q