Messing around with summation operators

[gcamilo]

Homework Statement

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 $$s_{2n}$$?

Homework Equations

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

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.

 

[Mark44]

Homework Statement

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 $$s_{2n}$$?

Homework Equations

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

The Attempt at a Solution

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

No

or

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

No

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

How would you write s₅ as a summation (not expanded)? How about s₁₀? Don't overthink this problem.

 

[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.