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Se considera suma S=1+2+3+...+n. Determinati numarul natural n, daca acesta reprezinta 5% din S.

Răspuns :

S=[tex] \frac{n(n+1)}{2} [/tex]
[tex] \frac{5}{100} S= \frac{1}{20} \frac{n(n+1)}{2} \\ n=\frac{1}{20} \frac{n(n+1)}{2} \\ 40n=n(n+1) \\ 40=n+1 \\ n=39[/tex]