Another way to write an infinite sum

Question

It is well known that $1+2+3+...+\infty =\frac{-1}{12} $.But if we write down $2$ as $1+1$, $3$ as $1+1+1$ and so on the sum should me written as $1+1+1+1+...+\infty$ and I don't thing has the same result as the first sum.So the thing is that that even if the sum converges to $\frac{-1}{12} $ and hence its terms can be arranged the result is clearly different, how is that possible ?(I tried to google it but nothing was useful, sorry if you think this is a dumb question)