Talk:Square pyramidal number: Difference between revisions

Revision as of 03:12, 23 June 2015

Revision as of 10:33, 7 November 2016

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:That does indeed seem to be a valid and nice proof (or at least something that could be made into a proof with a little more care about why the limit of the saw-tooth areas converges to the parabola area (in contrast to situations like [http://mathworld.wolfram.com/DiagonalParadox.html this one] for which the convergence argument doesn't work). But either it's not new or it doesn't (yet) belong here; see [[WP:NOR]]. So if you think it's new, the appropriate thing to do would be to get it properly published elsewhere first, so that the publication can be used as a [[WP:RS|reliable source]] here. Personally maintained web sites are not adequate for this purpose. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 22:48, 14 May 2013 (UTC)

:::I revised this demonstration, according to the preceding note of prof. David Eppstein. Its final edition was published. Overview and references are in the MATHID database at no. 06644800.

:::In the article in pdf format contained in the first figure, to step 2 of the discussion, is written the following general formula, derived with Excel:

_n

lim (Σ_n n^m)/n^m+1 = 1/(m+1) for each m of N

^n→∞¹

Note that the inverse limit (Σ fom zero to n) diverges, reproducing the sequence of natural numbers. <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Ancora Luciano|Ancora Luciano]] ([[User talk:Ancora Luciano|talk]] • [[Special:Contributions/Ancora Luciano|contribs]]) 15:25, 18 August 2013 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot-->

== Sum of the first ''n'' squares (geometrical proof) ==