http://www.ERBzine.com/mag

Bill Hillman

Editor and Webmaster

http://www.ERBzine.com ]]>

But all these supposedly mysterious values can be found by calculating the definite integral between 0 and -1 of the expression for the respective sum to the nth term (a.k.a. their partial sum expressions).

Here is a link to a really interesting ‘response’ video (it responds to the claims made in the video that is the subject of this discussion): https://www.youtube.com/watch?v=BpfY8m2VLtc

It shows what happens if you do the series manipulations rigorously (hint – you do not get -1/12) and it explains why other methods get this -1/12 result.

The response video claims this -1/12 result is the result of a mistake. The mistake is one of taking a function that applies to just positive whole numbers, manipulating it in ways that bring decimal numbers and negative numbers into play, and then interpreting the result as though it still relates to positive whole numbers.

]]>