Ta thấy: B là tích của 99 số âm
\(\Rightarrow B=\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{9}\right)\left(1-\dfrac{1}{16}\right)...\left(1-\dfrac{1}{100^2}\right)\)
\(=\dfrac{3}{2^2}.\dfrac{8}{3^2}.\dfrac{15}{4^2}...\dfrac{9999}{10^2}\)
\(=\dfrac{1.3}{2^2}.\dfrac{2.4}{3^2}.\dfrac{3.5}{4^2}...\dfrac{99.101}{100^2}\)
\(=\dfrac{1.2.3...98.99}{2.3.4...99.100}.\dfrac{3.4.5...100.101}{2.3.4...99.100}\)
\(=\dfrac{1}{2}.\dfrac{101}{100}\)
\(=\dfrac{101}{200}>\dfrac{1}{2}\)
\(\Rightarrow B< -\dfrac{1}{2}\).
ủa sao từ \(\dfrac{1}{2^2}-1\) lại thành \(1-\dfrac{1}{2^2}\) vậy bạn
