Question

\(\left(1+\dfrac{1}{1.3}\right).\left(1+\dfrac{1}{2.4}\right).....\left(1+\dfrac{1}{2019.2021}\right)\)

Answer 1

\(\left(1+\dfrac{1}{1.3}\right)\left(1+\dfrac{1}{2.4}\right).....\left(1+\dfrac{1}{2019.2021}\right)\)

\(=\dfrac{4}{1.3}.\dfrac{9}{2.4}.....\dfrac{4080400}{2019.2021}\)

\(=\dfrac{2.2}{1.3}.\dfrac{3.3}{2.4}.....\dfrac{2020.2020}{2019.2021}\)

\(=\dfrac{2.3.4.....2020}{1.2.3.....2019}.\dfrac{2.3.4.....2020}{3.4.5.....2021}\)

\(=2020.\dfrac{2}{2021}=\dfrac{4040}{2021}\)

Answer 2

`= 4/(1.3) xx 9/(2.4) xx .... xx 2020^2/(2019.2021)`

`= (2 xx 3 xx ... xx 2020)/(1 xx 2 xx ... xx 2019) xx (2 xx 3 xx ... xx 2020)/(3 xx 4 xx ... xx 2021)`

`= 2020/1 xx 2/2021`

`= 4040/2021`