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Daca N= 2+2^2+2^3+...+2^2007, scrieti ca putere a lui 2 numarul N+2.

Răspuns :

[tex]N=2+2^2+2^3+...+2^{2007}|(-2)\\ -2N=-2^2-2^3-...-2^{2008}\\ ...............................\\ -N=2-2^{2008}\\ N=2^{2008}-2 N+2=2^{2008}[/tex]