what is 1+1-1+1-1+1...?

The series is not absolutely convergent since the modulus of each term is 1 and the sum to infinity of 1 is divergent.

This shows that the order in which you add terms does matter, for example:

(1+1)-(1+1)-(1+1)-... = 2-2-2-... -> - infinity

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

(1+1) -1 + 1 - 1 ... = 2 -1+1-1+1...=2

Also using sum to infinity of geometric series formula (which is not necessarily valid since the ratio is not strictly between -1 and 1);

sum to infinity = a/(1-r) = 1/(1-(-1)) = 1/2

So the answer is, there is no real answer unless an order is specified.

1+1-1+1-1+1… = 1 + Σ[n=0 to n= infinity] (-1)^n
S(m) = Σ[n=0 to n=m] (-1)^n is a partial sum of series
S(0) = 1
S(1) = 0
S(2) = 1
S(3) = 0 ….

The series of partial sums 1, 0, 1, 0, … don’t have a finite limit.
=> 1 + Σ[n=0 to n= infinity] (-1)^n is a divergent series.

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2

1+1-1+1-1+1 or 1+1-1+1-1+1+....or1+1-1+1-1+1-....?
You see, unless you give in formula form, the n th term cannot be guessed from first few terms.
You must give it in the form 1 +(-1)^(n+1) or like.

2

1 + 1 - 1 + 1 - 1 + 1...
= 2 - 1 + 1 - 1 + 1...
= 1 + 1 - 1 + 1...
= 2 - 1 + 1...
= 1 + 1...
= 2...

2 ?

2 or 1

2

it's 2