Niste sume de puteri
Posted: Thu Jun 19, 2008 5:42 pm
Se da:
\( S_1 \ = \ 5 \ + \ 5^{^{2}} \ + \ 5^{^{3}} \ + \ 5^{^{4}} \ + \ ... \ + \ 5^{^{2008}}. \)
\( S_2 \ = \ 1 \ + \ \frac{1}{5} \ + \ \frac{1}{5^{^{2}}} \ + \ \frac{1}{5^{^{3}}} \ + \ ... \ + \ \frac{1}{5^{^{2007}}}. \)
Calculati: \( \sqrt{\frac{S_1}{S_2}} \).

\( S_1 \ = \ 5 \ + \ 5^{^{2}} \ + \ 5^{^{3}} \ + \ 5^{^{4}} \ + \ ... \ + \ 5^{^{2008}}. \)
\( S_2 \ = \ 1 \ + \ \frac{1}{5} \ + \ \frac{1}{5^{^{2}}} \ + \ \frac{1}{5^{^{3}}} \ + \ ... \ + \ \frac{1}{5^{^{2007}}}. \)
Calculati: \( \sqrt{\frac{S_1}{S_2}} \).