Question

[Music Alevis]

Cho   \(A=\left(\frac{1}{2^2}-1\right).\left(\frac{1}{3^2}-1\right).\left(\frac{1}{4^2}-1\right)...\left(\frac{1}{100^2}-1\right)\)

So sánh A với \(-\frac{1}{2}\)

Answer 1

[Lê Tài Bảo Châu]

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

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

\(A=-\left(\frac{1.2....99}{2.3...100}\right).\left(\frac{3.4....101}{2.3....100}\right)\)

\(A=-\left(\frac{1}{100}\right).\left(\frac{101}{2}\right)\)

\(A=\frac{-101}{200}>\frac{-1}{2}\)

Answer 2

[Lương Quang Vinh]

Thằng điên, có cái đầu bài cx chép sai thì làm ăn đếch j