Messing around with summation operators

AI Thread Summary
The discussion revolves around the confusion regarding changing summation operators in the expression s_{n} = ∑_{k=1}^n ((-1)^{k+1})/k. The user seeks assistance in determining s_{2n} and attempts various formulations, including s_{2n} = ∑_{k=1}^{2n} ((-1)^{2k+1})/2k and s_{2n} = ∑_{k=1}^{2n} ((-1)^{2k+2})/2k, but finds them incorrect. There is also a request for guidance on writing s5 and s10 as summations without overcomplicating the problem. The user expresses a desire to understand summation techniques better, feeling overwhelmed by the complexity of the topic. Understanding the correct manipulation of summation operators is essential for solving series proofs effectively.
gcamilo
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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.
 
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gcamilo said:

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
gcamilo said:
or

s_{2n}=\sum_{k=1} ^{2n} ((-1)^{2k+2})/2k
No
gcamilo said:
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.
 
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.
 

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