A=(1/2-1)(1/3-1)*...*(1/100-1)*(1/2+1)(1/3+1)*...*(1/100+1)
\(=\dfrac{-1}{2}\cdot\dfrac{-2}{3}\cdot...\cdot\dfrac{-99}{100}\cdot\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{101}{100}\)
\(=\dfrac{-1}{100}\cdot\dfrac{101}{2}=\dfrac{-101}{200}< -\dfrac{1}{2}\)