What is $(-1) + (-2) + (-3) + ... $? [closed]

The sum $(1+2+3+ ~ ...)$ does not equal $\frac{1}{12}$. It is pure non-sense statement pushed by people who wanted views and attention. Under no calculus course would that ever be approved as an answer to an infinite series question. In fact, people who are not familiar with calculus, and just rely on their intuition of an an infinite series is, would tell you that it diverges.

One has to go through some absurd mental gymnastics to "justify" this result. Just like I can also "justify" that, $$ 1 + 2^1 + 2^2 + 2^3 + 2^4 + ... = - 1$$ by using the $2$-adic metric on $\mathbb{Z}$.

Yes, I "justified" the result, but then I am entirely changing the natural meaning of that series. And therefore, I am intentionally deceiving people by telling them that. The original people who pushed that video should be ashamed of themselves, they knew exactly what they were doing, and they did it anyway.

If they simply said, "there is a strange circumstance in how you can humorously get $\frac{1}{12}$", then that would be valuable video. But instead they try to make it seem that people's own intuitive understanding of an infinite series is somehow wrong.