# Sum of a divergent series depends on the way how one performs the summation

Can some one explain the following sentence regarding summation of divergent series?

$$\text{Sum of a divergent series depends on the way how one performs the summation}.$$

What does mean it?

Can someone explain it by giving an example?

Thanks

• You might like to read this: en.wikipedia.org/wiki/Riemann_series_theorem – trancelocation Feb 22 '19 at 11:22
• The series $$1 - 1 + 1 - 1 +\ldots$$ comes to my mind. You can see it as $(1-1) + (1+1) + \dots$ or $1 - (1-1) - (1-1) \ldots$ – Matti P. Feb 22 '19 at 11:22

Try looking at $$\sum_{n=0}^\infty (-1)^n;$$ depending on how one groups the terms, one has $$0$$ or $$1$$:
$$1 + (-1 + 1) + (-1 + 1) \to 1\\ (1 - 1) + (1 -1) \cdots \to 0 .$$