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=A useful Geometric Series formula=
 
<math>\sum_{n = M}^N \alpha^n = \frac{\alpha^M - \alpha^{N-1}}{(1 - \alpha)}</math>
 
<math>\sum_{n = M}^N \alpha^n = \frac{\alpha^M - \alpha^{N-1}}{(1 - \alpha)}</math>
  
 
*What if <math>\alpha=1</math>????
 
*What if <math>\alpha=1</math>????
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*For what values of M and N does this formula hold? Can they both be negative? Does N need to be greater than M?
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[[More_on_geometric_series|Back to page on Geometric Series]]

Revision as of 08:41, 29 September 2010

A useful Geometric Series formula

$ \sum_{n = M}^N \alpha^n = \frac{\alpha^M - \alpha^{N-1}}{(1 - \alpha)} $

  • What if $ \alpha=1 $????
  • For what values of M and N does this formula hold? Can they both be negative? Does N need to be greater than M?

Back to page on Geometric Series

Alumni Liaison

Correspondence Chess Grandmaster and Purdue Alumni

Prof. Dan Fleetwood