William W. answered • 07/20/20
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Perhaps I'm not understanding your question but by definition, a series that diverges does not have a sum for an infinite number of terms. That's what "diverge" means. The more terms you add, the bigger the sum. Here's a graph for this series:
William W.
Well, there is a sum for a certain number of terms. Every series has that. In this case that sum changes for every term that is added in. A series that converges, has a sum for an infinite number of terms (as strange as that sounds).
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07/21/20
Lily S.
So what would the exact sum of n=1 Σ((1/n^2)-(1/n^3)) be? Would it be Σ1/n^2?
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07/21/20
William W.
Your expressions are all missing to upper limit. You say you are starting at n = 1 but is there a number or an infinity symbol on top of the Σ symbol? I'm assuming there is an infinity symbol, so the sum from n = 1 to infinity. For (1/n^2 - 1/n^3), we can combine the two fraction by getting a common denominator (n^3) and then it equates to Σ(n - 1)/n^3 but I'm not sure what you are trying to do so I don't know if I'm going down the right path. Perhaps you are looking for a certain number. To do so, you can use your calculator to do that.
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07/21/20
Lily S.
Ooooh. Thank you. So basically, only when it converges it has a sum?07/20/20