[tex]\displaystyle\\\text{Folosim formula: }\\2^0+2^1+2^2+2^3+...+2^n=2^{n+1}-1\\\\\text{Rezolvare}\\\\2^0+2^1+2^2+2^3+...+2^n=63\\\\2^{n+1}-1=63\\\\2^{n+1}-1=64-1~~~\Big| +1\\\\2^{n+1}=64\\\\64 = 2^6\\\\2^{n+1}=2^6\\\\n+1=6\\\\n=6-1\\\\\boxed{\bf n=5}[/tex]