Ecuatie in numere naturale
Posted: Mon Jan 28, 2008 7:28 pm
\( a) \) Demonstrati ca \( \forall n\in N \quad 1^3+2^3+...+n^3=\frac{n^2(n+1)^2}{4} \)
\( b) \) Gasiti multimile \( \left\{a_{1},a_{2},...,a_{n},...\right\}\subset{\mathbb N}^* \) stiind ca \( \forall n\geq1, \quad (a_{1}+a_{2}+...+a_{n})^2=a_{1}^3+a_{2}^3+...+a_{n}^3 \).
\( b) \) Gasiti multimile \( \left\{a_{1},a_{2},...,a_{n},...\right\}\subset{\mathbb N}^* \) stiind ca \( \forall n\geq1, \quad (a_{1}+a_{2}+...+a_{n})^2=a_{1}^3+a_{2}^3+...+a_{n}^3 \).