Question

Urgent!
$\sqrt{1 + 3 + 5 + ... + 2009 + 2011 + 2013}$ arati ca este rational

Answer 1

1+3+5+...+2013=(2013+1)*[ (2013-1)/2+1]/2=2014*1007/2=1007*1007=1007²

√1007²=1007∈N⊂Q, deci rational

Obs

de la 1 la 2013 avem  (2013-1)/2+1] numere deci  (2013-1)/2+1]/2 perechi de numere