Please help. How to write series in summation form?

1 can be written as 1/1, which then can be written as 1/2⁰

So the n'th term of this sequence is:

1/2^(n - 1)

Then we want to subtract every other term instead of adding everything, so when n is odd we want it to be positive and when n is even we want it negative.

We can multiply that (-1)^(n - 1)

to get it to work out that way.

Now each term is:

(-1)^(n - 1) / 2^(n - 1)

Since the exponents are the same, we can turn that to:

(-1/2)^(n - 1)

Now you can use that in summation form:

Σ (-1/2)^(n - 1)