Question

[le thi huyen]

cho A=(1/4-1).(1/9-1).(1/16-1)....(1/400-1). so sánh A với -1/2

Answer 1

[Phan Văn Hiếu]

\(A=\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right)\left(\frac{1}{16}-1\right)...\left(\frac{1}{400}-1\right)\)

\(A=\left(-\frac{3}{4}\right).\left(-\frac{8}{9}\right).\left(-\frac{15}{16}\right)...\left(-\frac{399}{400}\right)\)

\(A=\frac{-3.8.15...399}{4.9.16...400}\)

\(A=\frac{-3.2.4.3.5...21.19}{2^2.3^2.4^2...20^2}\)

\(A=\frac{-2.3.4...19}{2.3.4...20}.\frac{3.4.5...21}{2.3.4...20}\)

\(A=\frac{-1}{20}.\frac{21}{2}\)

\(A=\frac{-21}{40}< -\frac{1}{2}\)

vậy \(A< -\frac{1}{2}\)

Answer 2

[fuck everything]

thank you very much!!!!!!!