Question

Tính 

A = \(\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}....\frac{1000^2}{1000.1001}\)

Answer 1

\(A=\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}.....\frac{100^2}{1000.1001}\)

\(A=\frac{1.1.2.2.3.3.....1000.1000}{1.2.2.3.3.4.....1000.1001}\)

\(A=\frac{\left(1.2.3.....1000\right).\left(1.2.3.....1000\right)}{\left(1.2.3.4....1000\right).\left(2.3.4.....1001\right)}\)

\(A=\frac{1}{1001}\)

Answer 2

Ta có A=\(\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}.....\frac{1000^2}{1000.1001}\)

           =\(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{1000}{1001}\)

           =\(\frac{1.2.3.....1000}{2.3.4.....1001}\)

           =\(\frac{1}{1001}\)