Arithmetic Series 2k: Sum of (-1)^n

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Homework Help Overview

The discussion revolves around the sum of an arithmetic series defined by the expression Σ (-1)^n from n=1 to 2k. Participants explore the implications of the variable k and the nature of the series, which alternates between -1 and 1.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand how to express the series and questions whether k can be assumed as a constant. Other participants clarify that 2k indicates an even number of terms and discuss how to represent the series in written form.

Discussion Status

Participants have acknowledged that the sum of the series is 0 due to the even number of terms. Guidance has been offered on how to articulate the series in words, but there remains some uncertainty about the notation and representation.

Contextual Notes

There is a question regarding the assumption of k as a constant, and the original poster seeks clarification on how to properly write out the series.

resresd
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2k
Σ (-1)n
N=1
i am meant to write it out in full and i know that the answer is 0 which i think i understand as it will be -1+1-1+1 etc, but i don't know what to do about the k, it doesn't say that it is a constant, is it safe to assume it is anyway? and what do i do if it is?
thanks
resresd
 
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(-1)^n, right? Yes, k is a constant. 2k is the number of terms in -1+1-1+1... What's the sum? Hint: 2k is even.
 
yes sorry, i wrote it out in word and copy pasted it, the superscript obviously didn't show up. if 2k showa that the number of terms will be even then with the pattern of -1+1 the answere will be 0...how do i write it out though? is it just -1+1 with a recurring dot? can i do that?
 
The sum is 0, yes. Just write it using words, like '(-1+1)+(-1+1)+... k times =0+0+0+... k times=0'. Something like that.
 
Thanks
 

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