çarpanlara ayırma

Question

$2^{15}$ + $2^{14}$ + $2^{13}$ + ...   + 2 + 1  

İşleminin sonucu nedir?

Cvp: $2^{16}$ -1

Answer 1

$2^{15}+2^{14}+2^{13}+\dots+2+1 = \displaystyle \frac{(2-1)(2^{15}+2^{14}+2^{13}+\dots+2+1 )}{2-1}=\frac{2^{16}-1}{1}=2^{16}-1$