Question

1+3+3^2+3^3+3^4+.....+3^2011

Answer 1

Notam cu X = $1+3+3^2+3^3+3^4+.....+3^{2011}$


[tex]X = 1+3+3^2+3^3+3^4+.....+3^{2011}\\ 3X = 3 + 3^2 + 3^3 +...+3^{2012}[/tex]

Le scadem de jos in sus si obtinem:
[tex]2X = 3 + 3^2 + 3^3 +...+3^{2012} - (1+3+3^2+3^3+3^4+.....+3^{2011})\\ 2X = 3 + 3^2 + 3^3 +...+3^{2012} - 1 - 3 -3^2-...-3^{2011}\\ 2X = 3^{2012}-1 =\ \textgreater \ X = \frac{3^{2012} - 1}{2}[/tex]