i wanted to make a total sum of each series but there is no constant gap
between two members 1 4 9 ..
i cant make an expression of a sum
for the numerator and denominator
??
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.