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

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In summary, the conversation is about finding the sum of the sequence -1+1-1+1... with a variable k representing the number of terms. It is determined that the sum is 0, and it is safe to assume that k is a constant. The sum can be written as '(-1+1)+(-1+1)+... k times =0+0+0+... k times=0'.
  • #1
resresd
10
0
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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  • #2
(-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.
 
  • #3
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?
 
  • #4
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.
 
  • #5
Thanks
 

1. What is an arithmetic series?

An arithmetic series is a sequence of numbers where the difference between each consecutive number is constant. For example, in the arithmetic series 2, 5, 8, 11, 14, the common difference is 3.

2. What is (-1)^n in an arithmetic series?

(-1)^n is a term in the series that represents the alternating sign of each term. It means that every other term in the series will be multiplied by -1.

3. How do you find the sum of an arithmetic series with (-1)^n?

To find the sum of an arithmetic series with (-1)^n, you can use the formula S = (-1)^n * a, where S is the sum, n is the number of terms, and a is the first term in the series. You can also use the formula S = n * (a + l)/2, where l is the last term in the series.

4. Can (-1)^n be used in any arithmetic series?

Yes, (-1)^n can be used in any arithmetic series as long as the difference between each consecutive term is constant. It simply represents the alternating sign of each term.

5. How is an arithmetic series with (-1)^n different from a regular arithmetic series?

An arithmetic series with (-1)^n is different from a regular arithmetic series because it has an alternating sign for each term, while a regular arithmetic series has a constant sign for each term. It also results in a different sum compared to a regular arithmetic series.

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