Question

11. Scrieți numărul 2 013 ca o sumă de puteri distincte ale lui 2.

Answer 1

Răspuns:

2^10+2^9+2^8+2^7+2^6+2^4+2^3+2^2+2^0=1024+512+256+128+64+16+8+4+1=2013

Answer 2

$\it S=1+2+2^2+2^3+\ ...\ +2^n=2^{n+1}-1\\ \\ n=10 \Rightarrow S=2^{11}-1=2048-1=2047\\ \\ 2047-2013=34=2+32=2+2^5\\ \\ Pentru\ \ n=10,\ \ din\ \ suma\ \ S\ \ excludem\ \ 2+2^5,\ \ deci:\\ \\ 2013=1+2^2+2^3+2^4+2^6+2^7+2^8+2^9+2^{10}$

$\it 1=2^0$