Originally posted by Nicky4815Explain how S = 1-1+1-1+1-1+1... = 1-2-2-2-2-2-2... and I would be pleased.
Remember BODMAS addition parts of an equation are totalled before subtraction parts of the equation. So that means the equation simplifies to:
S=1-2-2-2-2-2-2...
So the sum to infinity is negative infinity.
You cannot ever sum an infinitive number of terms.
You can only sum more and more terms as the number of terms approaches infinity.
Then, and then only, you can deduce that the sum approaches infinity.
Infinity is not a number.
You CAN sum an inifitinite number of terms on occasion. For example
1 + 0.1 + 0.01 + 0.001 + .... = 10/9
However, the numbers in that series approach infinitely close to zero, a necessary requirement for an infinite sum to approach a finite value.
It isn't, however, sufficient in and of itself.
1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + ... does not converge on a finite value, even though its individual terms do approach infinitely close to zero. The main difference is how quickly the terms converge on zero.
With the stated sum (1 + 1 - 1 + 1 - 1 + 1 - 1 + ...), you have a different problem. Depending on how you group the terms, you could end up with an answer of 0 or 1 (or anywhere in between), meaning that the sum of the series does not converge at all, not even towards an infinite value!
Here's a similar sort of problem.
Imagine there is an automated light bulb. It starts off, turns itself on in one hour, turns itself off 30 minutes after that, and thereafter changes state in half the interval of the preceding change of state. In 2 hours will it be on or off?