Question

G=(1-1/4)*(1-1/9)*(1-1/16)*(1-1/25)*(1-1/36)

Answer 1

\(\frac{2}{12}\)

Answer 2

\(\frac{7}{12}\)

mình nhầm

Answer 3

7/12 là đúng nhé

Answer 4

\(G=\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{16}\right)\left(1-\frac{1}{25}\right)\left(1-\frac{1}{36}\right)\)

\(=\frac{2^2-1}{2^2}.\frac{3^2-1}{3^2}.\frac{4^2-1}{4^2}.\frac{5^2-1}{5^2}.\frac{6^2-1}{6^2}\)

\(=\frac{1.3}{2^2}.\frac{2.4}{3^2}.\frac{3.5}{4^2}.\frac{4.6}{5^2}.\frac{5.7}{6^2}\)

\(=\frac{1.2.3.4.5}{2.3.4.5.6}.\frac{3.4.5.6.7}{2.3.4.5.6}\)

\(=\frac{1}{6}.\frac{7}{2}\)

\(=\frac{7}{12}\)

Answer 5

\(G=\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{16}\right)\times\left(1-\frac{1}{25}\right)\times\left(1-\frac{1}{36}\right)\)

\(=\frac{4-1}{2^2}\times\frac{9-1}{3^2}\times\frac{16-1}{4^2}\times\frac{25-1}{5^2}\times\frac{36-1}{6^2}\)

\(=\frac{1\times3\times2\times4\times3\times5\times4\times6\times5\times7}{2^2\times3^2\times4^2\times5^2\times6^2}\)

\(=\frac{\left(1\times2\times3\times4\times5\right)\times\left(3\times4\times5\times6\times7\right)}{\left(2\times3\times4\times5\times6\right)\times\left(2\times3\times4\times5\times6\right)}\)

\(=\frac{1\times7}{6\times2}\)

\(=\frac{7}{12}\)