### Infinity or -1/12?

I happened upon the Numberphile video being discussed here and as a non mathematician I am wondering something.

The infinite sum 1-1+1-1+1-1...

If it is an infinite series , infinite being without end.

A question : does an infinite series have a beginning?

If it is truly infinite then surely it should be written ...+1-1+1-1+1-1...

It seems the article places a forward limit on the infinite series in order to mathematically manipulate it.

Any comment would be welcome.

Also in terms of infinity , surely if a number / series is infinite , then its always infinite , and merely writing a description of it does not create the series , or build its value.

The infinite series described by 1 + 2+ 3 + 4+ 5 ...

Is this "created" by the writing of its description , or is it fully infinite and only the description is being "built" and the idea that the sum diverges is merely a guide to writing the description?

Just wondering :)

• Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.