Question

determinați n€ N astfel încât 2 la puterea 0 +2 la puterea 1+2 la puterea 2....+ 2 la puterea n=63

Answer 1

 

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