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         <math>\vdots</math>                  <math>\vdots</math>
 
         <math>\vdots</math>                  <math>\vdots</math>
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From the observation, we can assume the following formula is true:
  
 
<math>\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}</math>
 
<math>\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}</math>
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==Discussion==
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*Would somebody care to add these to the [[Collective_Table_of_Formulas]]? Perhaps one should create be a new page dedicated to summation formulas.
  
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S5.2_45
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[[2011_Fall_MA_181_Bell|Back to MA 181, Prof. Bell]]
<!-- \left(  \right) -->
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<!-- <math>  </math> -->
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<math>f\left( x \right)=2x^3</math>
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<math>
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\lim_{N\rightarrow\infty}\sum_{n=1}^Nf\left( x_n^* \right)\,\Delta x_n
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=\lim_{N\rightarrow\infty}\sum_{n=1}^N2\cdot\left( \dfracnN \right)^3\cdot\dfrac1N
 
</math>
 
 
[[Category:MA181Fall2011Bell]]
 
[[Category:MA181Fall2011Bell]]

Latest revision as of 04:17, 6 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 $

From the observation, we can assume the following formula is true:

$ \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} $


Discussion

  • Would somebody care to add these to the Collective_Table_of_Formulas? Perhaps one should create be a new page dedicated to summation formulas.

Back to MA 181, Prof. Bell

Alumni Liaison

Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett