Revision as of 18:24, 3 September 2008 by Huffmalm (Talk | contribs)

  • (a) Prove that $ 1 + x + x^2 + \ldots + x^{n-1} = \frac{1-x^n}{1-x} $ for $ x\neq1 $ and integer $ n\geq1 $.
  • (b) What is $ 1 + 2x + 3x^2 + \ldots +nx^{n-1} $? (Hint: differentiate (a))
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Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett