Proof Without Words: The Alternating Harmonic Series Sums to ln 2

  title={Proof Without Words: The Alternating Harmonic Series Sums to ln 2},
  author={Matthew Hudelson},
  journal={Mathematics Magazine},
  pages={294 - 294}
  • M. Hudelson
  • Published 1 October 2010
  • Mathematics
  • Mathematics Magazine
Summary We demonstrate graphically the result that the alternating harmonic series sums to the natural logarithm of two. This is accomplished through a sequence of strategic replacements of rectangles with others of lesser area. In the limit, we obtain the region beneath the curve y = 1/x and above the x-axis between the values of one and two. 
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