Question

rezultatul calcului 1+2^1+2^2+.....+2^9 este​

Answer 1

 

$\displaystyle\\\text{Folosim formula:}\\\\k^0+k^1+k^1+k^3+...+k^n=\frac{k^{n+1}-1}{k-1}}~~~~~~\text{(Daca primul exponent = 0.)}\\\\1+2^1+2^2+...+2^9=\\\\=2^0+2^1+2^2+...+2^9=\frac{2^{9+1}-1}{2-1}=\frac{2^{10}-1}{1}=\boxed{\bf2^{10}-1}\\\\\text{Pentru numere mari rezultatul ramane asa, dar 2 si 10 nu sunt mari.}\\\\\text{Hai sa calculam:}~~2^{10}-1=1024-1=\boxed{\bf1023}$