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\[\lim_{n \rightarrow \infty} \frac{ [\sum_{r=1}^{2n-1 }(sr-1 ]^3 }{[ \sum_{r=1}^{2n-1}(sr-1)^2]^2 }\]

Mathematics
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what the hell is that??
exand the summation inside ,, its arithmetic series, and constant. express it in compact form and do business with cube and square outside.
What is the difference between numerator and denom ? except for sq. and cube.

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\[\lim_{n \rightarrow \infty} \frac{ [\sum_{r=1}^{2n-1 }(sr-1 ]^3 }{[ \sum_{r=1}^{2n-1}(sr-1)^2]^2 }\]
[ (s-1) + (2s-1) +(3s-1) ...((2n-1)s -1) ]^3 -------------------------------------- [ (s-1)^2 + (2s-1)^2 ...... ((2n-1)s -1)^2 ]^2
Sr ---- = s1 , s2 , s3 , s4 ...................
numerator = [ s + 2s +3s .. (2n-1)s - (2n-1) ]^3 denominator = [ s^2 + (2s^2) ..((2n-1)s)^2 - 2s(1+2+3..(2n-1)) +(2n-1) ]^2 This should help ?

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