\(A=\left(\dfrac{1}{2^2}-1\right)\left(\dfrac{1}{3^2}-1\right)\left(\dfrac{1}{4^2}-1\right).....\left(\dfrac{1}{100^2}-1\right)\)
\(A=-\dfrac{3}{4}.-\dfrac{8}{9}.-\dfrac{15}{16}.....-\dfrac{9999}{10000}\)
\(A=\dfrac{-\left(1.3\right)}{2.2}.\dfrac{-\left(2.4\right)}{3.3}.\dfrac{-\left(3.5\right)}{4.4}......\dfrac{-\left(99.101\right)}{100.100}\)
Từ \(-1\) đến \(-99\) có: \(\left(99-1\right):1+1=99\)
Cộng thêm số \(-101\) tất cả có \(100\) số hạng
\(A=\dfrac{1.3.2.4.3.5....99.101}{2.2.3.3.4.4.....100.100}\)
\(A=\dfrac{1.2.3....99}{2.3.4....100}.\dfrac{3.4.5....101}{2.3.4....100}\)
\(A=\dfrac{1}{100}.\dfrac{101}{2}\)
\(A=\dfrac{101}{200}\)
\(\)
