# Messing around with summation operators

1. Dec 2, 2009

### gcamilo

1. The problem statement, all variables and given/known data

I'm just not sure how to change the operators in summation, can anyone help?

Let $$s_{n}=\sum_{k=1} ^n ((-1)^{k+1})/k$$

what is $$s_{2n}$$?

2. Relevant equations

$$s_{n}=\sum_{k=1} ^n ((-1)^{k+1})/k$$

3. The attempt at a solution

$$s_{2n}=\sum_{k=1} ^{2n} ((-1)^{2k+1})/2k$$

or

$$s_{2n}=\sum_{k=1} ^{2n} ((-1)^{2k+2})/2k$$

This is in order to figure out a series proof, I just think I am really naive.

2. Dec 2, 2009

### Staff: Mentor

No
No
How would you write s5 as a summation (not expanded)? How about s10? Don't overthink this problem.

3. Dec 4, 2009

### gcamilo

Thanks! I guess I tried to overthink, I've just seen people do amazing things with summation sings and sequences, I just tried to imitate.