1 - 1 + 1 - 1 + 1 - 1 + 1,.... till infinity, what's the result?

Question

is it a violation of associative rule?

(a + b) + c = a + (b + c)

well you see:

(1 - 1) + (1 - 1) + (1 - 1) + (1 - 1) + .... = 0

while

1 + ( - 1 + 1) + ( - 1 + 1) + ( - 1 + 1) +.... = 1

Just curious really...

I clicked the wrong button

Sorry

Answer 1

That is really a math question, not astronomy or space.

The term infinity in math is not what most people think. Math doesn't speak of infinity. It only speaks of things like "increases without bound" or "undefined" or something like that. Some series increase without bound, others converge to a limit, but this does neither. So I say it is just undefined, but you should really ask it in the math section.

Answer 2

To be more precise, the question is whether the series 1-1+1 ... converges to some number evenrually.

1-1=0
1-1+1=1
1-1+1-1=0
and so on.

So as the number of terms gets bigger and bigger the sum alternates between 0 and 1, not a single number. So the correct answer is to say that the series does not converge.

It is not a violation of the associative rule, because the associative rule doesn't say anything about infinite series! In general you have to be very careful when applying any simple mathematical concept to infinite series.

Answer 3

m not sure but since we are going towards right of the number line so accordingly whatever the infinity value has to be it will be positive(in this case 1)

so 0+1-1+1-1+1-1..+infinity(1)=2

yes if we take left side it may be the diff rent story...

i wonder if that makes any sense

Answer 4

It has no limit. It flips back a forth and you're arithmetic is wrong (sort of) . In the fisrt case, you use 8 ones and in the second, you only used 7.

Answer 5

The generating function is not continuous or differentiable so the series does not converge. In other words, the answer is undefined.

Answer 6

Nothin and somethin forever,so there!