Question

( 1+ \(\dfrac{1}{2010}\) ) x ( 1+ \(\dfrac{1}{2011}\) ) x ( 1+ \(\dfrac{1}{2012}\) ) x...x (1+ \(\dfrac{1}{2020}\))

Answer 1

\(\left(1+\dfrac{1}{2010}\right)\times\left(1+\dfrac{1}{2011}\right)\times...\times\left(1+\dfrac{1}{2020}\right)\)

=\(\dfrac{2011}{2010}\times\dfrac{2012}{2011}\times...\times\dfrac{2021}{2020}\)

=\(\dfrac{2021}{2010}\)

Answer 2

Ta có: \(\left(1+\dfrac{1}{2010}\right)\left(1+\dfrac{1}{2011}\right)\left(1+\dfrac{1}{2012}\right)\cdot...\cdot\left(1+\dfrac{1}{2020}\right)\)

\(=\dfrac{2011}{2010}\cdot\dfrac{2012}{2011}\cdot\dfrac{2013}{2012}\cdot...\cdot\dfrac{2021}{2020}\)

\(=\dfrac{2021}{2010}\)