Question

Fie A=2 la puterea 0 + 2 la puterea 1 + 2 la puterea 2 +......+ 2 la puterea 2013.
Demontrati ca A+1 e un patrat perfect

Answer 1

folosesti formula:
$2^0+2^1+2^2+...+2^n= 2^{n+1}-1$

$A= 2^{2014}-1$

$2^{2014}-1+1= 2^{2014}= 2^{1007*2}=( 2^{1007})^2$