The discussion revolves around rewriting a Riemann Sum statement involving the expression sum (lower i=0)(upper 2n) (i/n)^2 (1/n). The equation is confirmed to be a Riemann Sum, specifically represented as \sum_{i=0}^{2n}\frac{i^2}{n^3}. Participants seek clarity on the correct formulation and simplification of the sum of squares, particularly the series 1^3 + 2^3 + 3^3 + ... + (2n)^2.
1^2 + 2^2 + ... + n^2Students in calculus, mathematics educators, and anyone involved in understanding or teaching Riemann Sums and summation techniques.
[tex]\sum_{i=0}^{2n}\frac{i^2}{n^3}[/tex]cybercrypt13 said:Homework Statement
We were asked to identify and rewrite the following statement. Not sure how to do a sum sign here so will just write sum for it:
sum (lower i=0)(upper 2n) (i/n)^2 (1/n) = 1/n^3[ 1^3 + 2^3 + 3^3 + ... + (2n)^2
Do you know a formula for the sum of squares: 1+ 4+ 9+ 16+ ...?Homework Equations
I believe this is a Riemann Sum but not sure how to rewrite it.
The Attempt at a Solution
I have :
I'm still looking for how to rewrite.
Thanks,
glenn