(1-$\dfrac{1}{2²}$).(1-$\dfrac{1}{3²}$).(1-$\dfrac{1}{4²}$).....(1-$\dfrac{1}{9²}$)
=$\dfrac{3}{4}$.$\dfrac{8}{9}$.$\dfrac{15}{16}$.....$\dfrac{80}{81}$
=$\dfrac{1.3}{2.2}$.$\dfrac{2.4}{3.3}$.$\dfrac{3.5}{4.4}$.....$\dfrac{8.10}{9.9}$
=$\dfrac{1.3.2.4.3.5....8.10}{2.2.3.3.4.4.....9.9}$
=$\dfrac{5}{216}$