Question

Tính nhanh:         (1-1/4).(1-1/9).(1-1/16)..............(1-1/625)

Answer 1

\(\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{16}\right)......\left(1-\frac{1}{625}\right)\)

= \(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}......\frac{624}{625}\)

= \(\frac{1.3.2.4.3.5.....24.26}{2.2.3.3.4.4......25.25}\)

= \(\frac{\left(1.2.3....24\right)\left(3.4.5....26\right)}{\left(2.3.4....25\right)\left(2.3.4....25\right)}\)

= \(\frac{26}{25.2}\)

= \(\frac{13}{25}\)