Where is the mistake in proving 1+2+3+4+… = -1/12? https://www.youtube.com/watch?v=w-I6XTVZXww#t=30
As I watched the video on YouTube of proving sum of $$1+2+3+4+\cdots= \frac{-1}{12}$$
Even we know that the series does not converge.
First I still can't prove what wrong in infinite sum of $$1-1+1-1+1+\cdots= \frac{1}{2}$$
and I want to know more about of what mistake did they make in the video.
I did research on our forum about this topic. But still not clearly understand about of that proving.
Thank you.
(Sorry about my bad English )

In proving that 1-1+1-1+... = 1/2, you add two divergent series, which can sometimes produce a convergent series. However, here, (I'll mark our sum I = 1-1+1-1+...) I+I = 2*I = 2-2+2-2+... and that still diverges, although we shifted one of those to get that 2*I = 1. That's a contradiction.
That is the main problem with this proof. 
Hope this helped!
