# Riemman Sum

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• Feb 3rd 2009, 03:50 PM
Larrioto
Riemman Sum
The limit as x approches infinity of the sum from i=1 to n of :

$(1+\frac{i}{n})^3$
• May 28th 2009, 12:52 PM
Media_Man
Divergent
$\lim_{n\rightarrow\infty}\sum_{i=1}^n(1+\frac{i}{n })^3$ = $\lim_{n\rightarrow\infty}\sum_{i=1}^n\frac1{n^3}(n ^3+3n^2i+3ni^2+i^3)$= $\lim_{n\rightarrow\infty} 1+\frac3n\sum_{i=1}^ni+\frac3{n^2}\sum_{i=1}^ni^2+ \frac3{n^3}\sum_{i=1}^ni^3$ = $\lim_{n\rightarrow\infty} 1+\frac3n\frac{n(n+1)}2+\frac3{n^2}\frac{n(n+1)(2n +1)}6+\frac3{n^3}\frac{n^2(n+1)^2}4$ = $\infty$

This limit diverges. What was the original problem?