1 + 2 + 3 + 4 + 5 + ... = -1/12

Oy mate! Don't you have a pint of cider to drink in a cozy pub somewhere instead of producing videos of such bollocks?

The series $\sum_{n=1}^\infty n$ is divergent, so you can't say anything about its sum. For more info on the 1 - 1 + 1 - 1 +1 ... see: http://en.wikipedia.org/wiki/History_of_Grandi's_series This quote from the page is telling:

   G. H. Hardy dismisses both of these as "little more than nonsense."

Properties of numbers change at infinity. It is not conceivable to me, we can use normal arithmetic operations on quantities tending to infinity. For example, consider this...

   9999999999........... infinity
  -9999999999........... infinity
   -------------------------
   00000000000............ infinity
   -------------------------

Now, subtracting infinite numbers from infinite numbers should give a infinite result. All we have is infinite zeros here, which cannot be inifinity.