Question

[emily]

Cho A = \(\left(\frac{1}{2^2}-1\right).\left(\frac{1}{3^2}-1\right).....\left(\frac{1}{100^2}-1\right)\)

So sánh A với \(\frac{-1}{2}\)

Giúp gấp vs!!!!

Answer 1

[ღ๖ۣۜLinh's ๖ۣۜLinh'sღ] ★we are one★]

\(A=\frac{-3}{4}.\frac{-8}{9}......\frac{-9999}{1000}\)

\(=-\frac{1.3}{2.2}.\frac{2.4}{3.3}....\frac{99.101}{100.100}\)

\(=-\frac{1.2.3...99}{2.3...100}.\frac{3.4...101}{2.3...100}\)

\(=-\frac{1}{100}.\frac{101}{2}=-\frac{101}{200}< \frac{-100}{200}=\frac{-1}{2}\)

VẬY \(A< \frac{-1}{2}\)