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're on the right track! The expression you have written using summation notation is correct. The sum you're trying to express is an alternating series, where the signs of the terms alternate between positive and negative.
To determine the value of n, which represents the number of terms, we need to consider the pattern of the series. In this case, the terms in the series are in the form 1/n, and you want to find the sum of 3n terms.
Since each term in the series corresponds to a value of k in the summation notation, we can equate the value of k to the number of terms n. That means we can rewrite the equation as:
((-1)^(n+1))/n
Now, to find the value of n, we need to consider what happens to the term 1/n as n increases. We see that as n increases, the terms become smaller and approach zero. In this case, we want to find the number of terms where the series stops, which is 3n terms.
To find the value of n, you can set the term 1/n less than or equal to a small positive value, such as 0.001, and solve for n:
1/n <= 0.001
This can be rearranged to:
n >= 1/0.001
n >= 1000
So, the value of n should be the smallest integer greater than or equal to 1000. In this case, n = 1000.
Therefore, the expression using summation notation for the sum of the first 3n terms would be:
∑ ((-1)^(k+1))/k from k = 1 to 1000