Đáp án:
Giải thích các bước giải:
# Jenny2710
(1- $\frac{1}{2}^{2}$) . ( 1-$\frac{1}{3}^{2}$ ) ....(1-$\frac{1}{9}^{2}$)
= (1- $\frac{1}{4}$ ).(1-$\frac{1}{9}$ )...(1-$\frac{1}{81}$ )
= $\frac{3}{4} . \frac{8}{9}...\frac{80}{81}$
= $\frac{1.3}{2^{2}} . \frac{2.4}{3^{2}}...\frac{8.10}{9^{2}}$
= $\frac{1.3.2.4...8.10}{2^{2}.3^{2}...9^{2}}$
= $\frac{1.2.3...8}{2.3...8.9} . \frac{3.4.5...10}{2.3...8.9}$
= $\frac{1}{9} . \frac{10}{2}$
= $\frac{10}{18}$ = $\frac{5}{9}$