Question

Tính \(A=\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{16}\right)...\left(1-\frac{1}{900}\right)\)

 

Answer 1

=\(\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}...\cdot\frac{899}{900}=\frac{1.3}{2.2}\cdot\frac{2.4}{3.3}\cdot\frac{3.5}{4.4}...\cdot\frac{29\cdot31}{30\cdot30}=\frac{1.2.3.4...29\cdot3.4.5...30.31}{2.2.3.3.4.4...30.30}=\frac{1.31}{2.30}=\frac{31}{60}\)

Answer 2

\(A=\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}....\frac{899}{30^2}=\frac{\left(1.3\right).\left(2.4\right).\left(3.5\right)...\left(29.31\right)}{\left(2.3.4...30\right).\left(2.3.4...30\right)}=\frac{\left(1.2....29\right).\left(3.4.5...31\right)}{\left(2.3.4...30\right).\left(2.3.4..30\right)}=\frac{1.31}{30.2}=\frac{31}{60}\)

Answer 3

= \(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}....\frac{899}{900}\)

= \(\frac{3}{2.2}.\frac{8}{3.3}.\frac{15}{4.4}.....\frac{899}{9.100}\)

= (bạn tự giải tiếp nhé)