\(\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{16}\right)\times\left(1-\frac{1}{25}\right)\times\left(1-\frac{1}{36}\right)\)
\(=\)\(\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times\frac{24}{25}\times\frac{35}{36}\)
\(=\)\(\frac{3\times8\times15\times24\times35}{4\times9\times16\times25\times36}\)
\(=\)\(\text{}\text{}\text{}\text{}\text{}\text{}\frac{\text{}\text{}\text{}\text{}\text{}\text{}3\text{}\text{}\text{}\text{}\text{}\text{}\times4\text{}\text{}\text{}\text{}\text{}\text{}\times2\text{}\text{}\text{}\text{}\text{}\text{}\times5\text{}\text{}\text{}\text{}\text{}\text{}\times3\text{}\text{}\text{}\text{}\text{}\text{}\times6\text{}\text{}\text{}\text{}\text{}\text{}\times4\text{}\text{}\text{}\text{}\text{}\text{}\times5\text{}\text{}\text{}\text{}\text{}\text{}\times7}{4\text{}\text{}\text{}\text{}\text{}\text{}\times3\text{}\text{}\text{}\text{}\text{}\text{}\times3\text{}\text{}\text{}\text{}\text{}\text{}\times8\text{}\text{}\text{}\text{}\text{}\text{}\times2\text{}\text{}\text{}\text{}\text{}\text{}\times5\text{}\text{}\text{}\text{}\text{}\text{}\times5\text{}\text{}\text{}\text{}\text{}\text{}\times6\text{}\text{}\text{}\text{}\text{}\text{}\times6}\)
\(=\)\(\frac{7\text{}\text{}\text{}\times4}{8\times6}\)
\(=\)\(\frac{7\times4}{4\times2\times6}\)
\(=\)\(\frac{7}{2\times6}\)
\(=\)\(\frac{7}{12}\)
