Question

Calculați:
$\sqrt{4x + 1}$
unde
$x = 1 + 5 + {5}^{2} + {5}^{3} + ... + {5}^{2012} + {5}^{2013}$
Urgent!!!! Dau COROANAA!!!!

Answer 1

Răspuns:

Explicație pas cu pas:

$\texttt{Se inmulteste x cu 5 }:\\5x=5+5^2+5^3+\ldots +5^{2014}\\\texttt{Scadem x din 5x}:\\5x-x= (5+5^2+5^3+\ldots+5^{2014})-(1-5-\ldots-5^{2013})\\4x=5^{2014}-1\\\sqrt{4x+1}=\sqrt{5^{2014}-1+1}=\sqrt{5^{2014}}=\boxed{5^{1007}}$