Question

Tính:

a, \(\dfrac{2}{1.3}\)+\(\dfrac{2}{3.5}\)+\(\dfrac{2}{2019.2021}\)

b, \(\dfrac{3}{2}\)+\(\dfrac{3}{2^2}\)+\(\dfrac{3}{2^3}\)+.......+\(\dfrac{3}{2^{2018}}\)

tk cho bạn nhanh nhất❤

Answer 1

\(\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{2}{2019.2021}\)

= \(2.\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{2}{2019.2021}\right)\)

= \(1.\left(\dfrac{1}{1.3}+\dfrac{1}{3.5}+...+\dfrac{1}{2019.2021}\right)\)

= \(1.\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{2019}-\dfrac{1}{2021}\right)\)

= \(1.\left(1-\dfrac{1}{2021}\right)\)

= \(1.\dfrac{2020}{2021}\)

= \(\dfrac{2020}{2021}\)