Dear Steele,

This is becoming quite a learning experience
and fun as well. Thank You for opening up a whole
new world for me.

Would this be leading to a dissertation on the difference between the Euclidian & Lafayette Systems of Mathematics, thence on to Lyndon La Rouche connection with the Citizens electoral Council. Would it steelie? I would have thought that Lyndon La Rouche would have been to extreme right for you.

Thanks SR just minutes ago in ABC NEWS 24 a maths man spoke of the hidden maths in that show.
Homer for one has been seen writing obscure [to us] maths problems and other too including Arboo,

I fundamentally believe the world makes sense even if it is not intuitive. After looking at this question more closely I am satisfied that the result is misleading.
The salient points are the natural numbers are defined as positive whole numbers therefore the result of the calculation can not be negative or to put another way if you take all the apples in the world and add them together you can not end up with -1/12 of an orange. The chosen staring point for the calculation is arbitrary I.E zero. The calculation could just as well have started at -3 in which case the series would look like this -3-2-1-0+1+2+3. My conclusion is the original formula refers to N meaning a whole number and not N meaning a positive whole number.

Using the same logic, I can get infinity = -1/6 or -1/24 etc.

The reality is that ignoring the end as n-> infinity makes the calculation meaningless.

I think the flaw in the system the guy uses is that he shifts the 2nd line to the right. Why?

Interesting It like the problem of 2=2=5, is it.

In 75 I did a Basic Electronics Course by Correspondence through Stotts College. (now defunct) I was doing some cleaning out over Christmas & ran across the Course. I though to my self, "I should run through that again as a refresher." So I started on New years Day. Very interesting & lots & lots of Maths, Graphs, Algebra & Cartesian Co-ordinates.