I should be writing math textbooks.<br>
What does anyone use this particular equality for?<br>
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<br><div><span class="gmail_quote">On 10/30/05, <b class="gmail_sendername">Mathieu Bouchard</b> <<a href="mailto:matju@artengine.ca">matju@artengine.ca</a>> wrote:</span><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
On Sat, 29 Oct 2005, Chuckk Hubbard wrote:<br><br>> Just a note, I came up with a pretty obvious proof for:<br>> SUM (k=0 to N-1) i^k = (i^N - 1) / (i - 1)<br>> (i - 1) (i^0 + i^1 + i^2 + .... + i^(N-1))<br>> =
<br>> -i^0 + i^1 - i^1 + i^2 - i^2 ... + i^(N-1) - i^(N-1) + i^N<br>> = i^N - 1<br>> All the terms cancel except the lowest and highest powers of i.<br><br>That's the same proof that is used in all math textbooks.
<br><br>____________________________________________________________________<br>Mathieu Bouchard - tél:+1.514.383.3801 - <a href="http://artengine.ca/matju">http://artengine.ca/matju</a><br>Freelance Digital Arts Engineer, Montréal QC Canada
<br></blockquote></div><br><br clear="all"><br>-- <br>"It is not when truth is dirty, but when it is shallow, that the lover of knowledge is reluctant to step into its waters."<br>-Friedrich Nietzsche, "Thus Spoke Zarathustra"