Question

Calculati:

Radical din 2x+1 unde x=1+3+3la puterea a 2+ 3la puterea a3+ ... + 3 la puterea2013

Answer 1

[tex]x=1+3+3^2+3^3+....+3^{2013}|(-3)\\ -3x=-3-3^2-3^3....-3^{2014}\\ ..................................................+\\ -2x=1-3^{2014}\\ 2x=3^{2014}-1\\ x=\frac{3^{2014}-1}{2}\\ \sqrt{2x+1}=\sqrt{2*\frac{3^{2014}-1}{2}+1}=\sqrt{3^{2014}-1+1}=\\ =\sqrt{3^{2014}=3^{1007}[/tex]