\(T=\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{16}\right)\times...\times\left(1-\frac{1}{625}\right)\)
\(=\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times...\times\frac{624}{625}\)
\(=\frac{1.3}{2.2}\times\frac{2.4}{3.3}\times\frac{3.5}{4.4}\times...\times\frac{24.26}{25.25}\)
\(=\frac{\left(1.2.3....24\right).\left(3.4.5....26\right)}{\left(2.3.4....25\right).\left(2.3.4.....25\right)}=\frac{1.26}{25.2}=\frac{13}{25}\)