Question

completați cu trei factori următorul sir 1/3 1/15 1/35 1/63 1/99....​

Answer 1

Explicație pas cu pas:

$\frac{1}{3} ; \frac{1}{15} ; \frac{1}{35} ; \frac{1}{63} ; \frac{1}{99} ...$

observăm:

$\frac{1}{1 \times 3} ; \frac{1}{3 \times 5} ; \frac{1}{5 \times 7} ; \frac{1}{7 \times 9} ; \frac{1}{9 \times 11} ...$

=>

$\frac{1}{11 \times 13} = \frac{1}{143} \\ \frac{1}{13 \times 15} = \frac{1}{195} \\ \frac{1}{15 \times 17} = \frac{1}{255}$

=>

$\frac{1}{3} ; \frac{1}{15} ; \frac{1}{35} ; \frac{1}{63} ; \frac{1}{99} ; \frac{1}{143} ; \frac{1}{195} ; \frac{1}{255} ...$