integration - 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 )