Express the sum using summation notation:

1 - 1/2 + 1/3 - 1/4 + 1/5 - ... (to 3n terms)

If I'm doing this right so far, with k=1 (the number on bottom of the sigma), the equation after the sigma would be

((-1)^(k+1)) / k

I'd be able to figure out the term on top of the sigma, n, if I knew the value, but I don't understand how to get it because of the way it is worded. Please help, and correct me if what i've done so far is wrong.

You are on the right track! The formula you have written for each term of the series, ((-1)^(k+1))/k, is correct.

To express this series using summation notation, let's break it down step by step:

1. First, let's consider the number of terms in the series, denoted as 3n. This means that we want to sum up to a total of 3n terms.

2. Next, let's find the upper limit of the summation, which is the value of n that corresponds to 3n terms. To determine this, we have to solve the equation 3n = total number of terms.

3. In this case, the total number of terms is not explicitly given. However, we can see that each term in the series has a denominator that is increasing by 1. So, we can infer that the total number of terms is twice the value of n. This is because each term has both a positive and negative component. Therefore, the total number of terms is 2 * 3n = 6n.

4. Now that we know the total number of terms is 6n, we can express the summation using this value as the upper limit. To do this, we replace the term "n" in the formula with "6n".

Therefore, the summation notation for the given series is:
Σ [((-1)^(k+1))/k] from k = 1 to 6n.

It is important to note that in summation notation, the term "k" represents the index of the summation and it starts from the lower limit (in this case, 1) and goes up to the upper limit (in this case, 6n).

So, the expression can be written as:
Σ [((-1)^(k+1))/k] from k = 1 to 6n.