Question

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

Answer 1

what the hell is that??

Answer 2

exand the summation inside ,, its arithmetic series, and constant. express it in compact form and do business with cube and square outside.

Answer 3

What is the difference between numerator and denom ? except for sq. and cube.

Answer 4

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

Answer 5

[ (s-1) + (2s-1) +(3s-1) ...((2n-1)s -1) ]^3
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[ (s-1)^2 + (2s-1)^2 ...... ((2n-1)s -1)^2 ]^2

Answer 6

Sr ---- = s1 , s2 , s3 , s4 ...................

Answer 7

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 ?