Question

cho A=(\(\dfrac{1}{2^2}-1\))(\(\dfrac{1}{3^2}-1\))(\(\dfrac{1}{2^2}-1\))...........(\(\dfrac{1}{100^2}-1\)).SO sánh A với \(\dfrac{-1}{2}\)

Answer 1

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Answer 2

A=(1/2^2-1) (1/3^2-1) (1/4^2-1) .... (1/100^2-1)

A=(1/2^2-2^2/2^2) (1/3^2-3^2/3^2) ...... (1/100^2-100^2/100^2)

A=1-2^2/2^2 . 1-3^2/3^2 .... 1-100^2/100^2

A=-(2^2-1/2^2 . 3^2-1/3^2 ..... 100^2-1/100^2)

A=-(1.3/2^2 x 2.4/3^2 ..... 99.101/100^2)

A=-(1.3.2.4.....99.101/2.2.3.3.....100.100)

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

A=-101/200 < -1/2