Confusion in Ramanujan's $1+2+3+...=\frac{-1}{12}$

Question

It is famous by Ramanujan that $1+2+3+...=\frac{-1}{12}$.
But what is the value of $1+1+1=....$?

I was thinking that $2=1+1$ and $3=1+1+1$ and so on...So does this mean that $1+1+1+...=\frac{-1}{12}$.

It means that when you have infinity you can do anything and everything. Please explain this

Answer 1

The axioms used for this derivation don't assume that $$1 + (1+1) + (1+1+1) + (1+1+1+1) + \dots = 1 + (1 + (1 + (1 + \dots$$

In fact the freedom to arbitrarily regroup terms is not assumed for series in general, let alone tricky things like this.