Question

cho A=(1/2² -  1)(1/3² -  1).......(1/2020²  -  1)    và B= -1/2

Hãy so sánh A và B

Answer 1

\(A=\left(\dfrac{1}{2^2}-1\right)\left(\dfrac{1}{3^2}-1\right).....\left(\dfrac{1}{2020^2}-1\right)\)

\(A=\left(\dfrac{1}{4}-1\right)\left(\dfrac{1}{9}-1\right).....\left(\dfrac{1}{4080400}-1\right)\)

\(A=-\left(\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.....\dfrac{2019.2021}{2020.2020}\right)\)

\(A=-\left(\dfrac{1.2.3.....2019}{2.3.....2020}.\dfrac{3.4.5.....2021}{2.3.4.....2020}\right)\)

\(A=-\left(\dfrac{1}{2020}.\dfrac{2021}{2}\right)=-\dfrac{2021}{4040}< -\dfrac{1}{2}\)