Question

Calculati 3+2a,stiind ca a=3+3 la puterea a 2+3la puterea a3........+3la puterea a2011.

Answer 1

a = 3 + 3² + 3³ +.........+3^2011
3a = 3² + 3³ +.............+3^2012
3a - a = 2a = 3^2012 - 3      a = (3^2012 - 3) / 2
3 + 2a = 3 + 3^2012 - 3 = 3^2012

Answer 2

$3+2\cdot 3+2\cdot 3^2+....+2\cdot 3^{2011}= \\ 3\cdot 3+2\cdot3^2+....+2\cdot3{2011}= \\ 3^2+2\cdot3^2+2\cdot 3^3+....+2\cdot 3{2011}= \\ 3\cdot3^2+2\cdot 3^3+.....+2\cdot 3{2011}= \\ 3^3+2\cdot3^3+2\cdot 3^4+....+2\cdot 3^{2011}= \\ .... \\ 3^{2011}+2\cdot3^{2011}=3\cdot3^{2011}=3^{2012}$