| Line 16: | Line 16: | ||
S5.2_45 | S5.2_45 | ||
<!-- \left( \right) --> | <!-- \left( \right) --> | ||
| − | <!-- --> | + | <!-- <math> </math> --> |
<math>f\left( x \right)=2x^3</math> | <math>f\left( x \right)=2x^3</math> | ||
<math> | <math> | ||
| − | + | \begin{split} | |
| − | + | &\lim_{N\rightarrow\infty}\sum_{n=1}^Nf\left( x_n^* \right)\,\Delta x_n | |
| − | + | \end{split} | |
</math> | </math> | ||
[[Category:MA181Fall2011Bell]] | [[Category:MA181Fall2011Bell]] | ||
Revision as of 15:04, 5 September 2011
Homework 2 collaboration area
Here's some interesting stuff:
$ \sum_{n=1}^N 1 = \dfrac11N $
$ \sum_{n=1}^N n = \dfrac12N\left(N+1\right) $
$ \sum_{n=1}^N n\left(n+1\right) = \dfrac13N\left(N+1\right)\left(N+2\right) $
$ \vdots $ $ \vdots $
$ \sum_{n=1}^N \dfrac{\left(n+k\right)!}{\left(n-1\right)!} = \dfrac1{k+2}\cdot\dfrac{\left(N+k+1\right)!}{\left(N-1\right)!}\quad \mathrm{for}\;k\in\mathbb{N} $
S5.2_45
$ f\left( x \right)=2x^3 $
$ \begin{split} &\lim_{N\rightarrow\infty}\sum_{n=1}^Nf\left( x_n^* \right)\,\Delta x_n \end{split} $
