Question

[Thi Bùi]

TÍNH K = [ \(\frac{1}{2^2}\)-1][\(\frac{1}{3^2}\)-1][\(\frac{1}{4^2}\)-1]..........[\(\frac{1}{100^2}\)-1]

                                 LÀM hộ tớ nhé , tớ tick cho

Answer 1

[Lê Tài Bảo Châu]

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

\(=-\left(\frac{1.3}{2.2}\right)\left(\frac{2.4}{3.3}\right)\left(\frac{3.5}{4.4}\right)....\left(\frac{99.101}{100.100}\right)\)

\(=-\left(\frac{1.2.3...99}{2.3.4...100}\right)\left(\frac{3.4.5...101}{2.3.4...100}\right)\)

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

\(=-\frac{101}{200}\)

Answer 2

[Nguyễn Diệu Hương]

K = -3/4.-8/9......-9999/10000

= -(3/4.8/9....9999/10000)

= -(1.3.2.4.....99.101/2^2.3^2.....100^2)

= -(1.2.3.....101).(3.4.5....99)/(2.3.4.....100).(2.3.4....100)

= -(101/2.100)

= -101/200