lt (n tending to infinity)[{1^2+2^2+3^2+........+(2n)^2}/{2^2+4^2+......+(2n)^2}-1]
now,1^2+2^2+3^2+......+(2n)^2=2n*(2n+1)*(4n+1)/6.
&,2^2+4^2+......+(2n)^2=2^2{1^2+2^2+3^2+.....+n ^2}
=2^2*n*(n+1)*(2n+1)/6
hence,lt(n--->infinity)[(2*2*4)/(4*1*2)-1]
=1.
I, clearly wrongly, assumed from this that you were familiar with the results for and and it was simply the 'constant gap' that was causing the problem.
If that's not the case, then I don't see how you could do the question, in which case I don't see why you would be given it in the first place.