Remainder

remainder is zero

it forms a series whose 2011 term is:
1+3+9+27+81+.............2010 terms
and then a_{2010}=\frac{3^{2010}-1}{2}
then if we divide 3^5 by 22 then remainder is 1 and if we divide 3^10,3^15,3^20....,3^2010 by 22 then also remainder is 1 ..... so if we subtract 1 from 3^2010 then remainder becomes 1-1=0 so it is disible by 11