Question

Answer 1

\(A=\left(\dfrac{1}{2^2}-1\right)\left(\dfrac{1}{3^2}-1\right)\left(\dfrac{1}{4^2}-1\right)....\left(\dfrac{1}{100^2}-1\right)\\ =\dfrac{-1.3}{2^2}.\dfrac{-2.4}{3^2}.\dfrac{-3.5}{4^2}..\dfrac{-99.101}{100^2}\\ =-\dfrac{1}{2}.\dfrac{101}{100}=-\dfrac{101}{200}< -\dfrac{1}{2}\Rightarrow A< -\dfrac{1}{2}\)