Look at this excerpt from the Algorithm Design Manual by Skiena, 2nd Edition

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The sum of the first $n$ even integers? Surely, the two sums given do not include only even numbers, right? Is this a mistake on the author's part, or am I missing something?

  • 1
    $\begingroup$ Looks like a mistake, yes. Either they wanted to use $2i$, which simplifies to 2 * what they write then. Or, the "even" should not be in the sentence. I consider the second more likely since the second half of the sentence doesn't make sense for only even integers, either. $\endgroup$
    – Raphael
    Oct 12 '17 at 10:35
  • $\begingroup$ What's intended is "The sum of the first even $n$ integers ... ". As written, it's in error. $\endgroup$
    – Thumbnail
    Oct 12 '17 at 17:31

This is an explanation for the Gaussian sum formula (funfact: in German it is called "little Gauss"). Hence, as you recognized, the even here is not correct.

The equality of these sums can be shown inductively or simply by putting them into Wolframalpha

The "even" case works like Raphael stated, but doesn't seem to have any intellectual value.


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