Problema 1, lista scurta 2009
Posted: Sun Apr 19, 2009 8:33 pm
Fie numerele naturale nenule \( a_1,a_2,...,a_{n+1} \) si \( k \) astfel incat :
\( a_1\le a_2\le ...\le a_{n+1}. \)
Demonstrati inegalitatea :
\( \left\lfloor \frac{a_2-a_1}{k}\right\rfloor+\left\lfloor \frac{a_3-a_2}{k}\right\rfloor+...+\left\lfloor \frac{a_{n+1}-a_{n}}{k}\right\rfloor+n-1\ge \left\lfloor \frac{a_{n+1}-a_1}{k}\right\rfloor \)
Manea Cosmin si Petrica Dragos, Pitesti
\( a_1\le a_2\le ...\le a_{n+1}. \)
Demonstrati inegalitatea :
\( \left\lfloor \frac{a_2-a_1}{k}\right\rfloor+\left\lfloor \frac{a_3-a_2}{k}\right\rfloor+...+\left\lfloor \frac{a_{n+1}-a_{n}}{k}\right\rfloor+n-1\ge \left\lfloor \frac{a_{n+1}-a_1}{k}\right\rfloor \)
Manea Cosmin si Petrica Dragos, Pitesti