For the series such that: [itex]\Sigma _{n=1} ^{\infty} a_n =\Sigma _{n=1} ^{\infty} b_n[/itex] A certain theorem says that these series are equal even if [itex]a_n = b_n[/itex] only for n>m. That is, even if two infinite series differ for a finite number of terms, it will still converge for the same sum. I am thinking that with this, we can extend the value of the starting index to include even the negative integers, and this will also extend the familiar operation that we do with finite summations where let's say:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\Sigma _{k=1} ^{5} a_k =\Sigma _{k=2} ^6 a_{k-1} [/itex] To its infinite series analog:

[itex]\Sigma _{k=1} ^{\infty} a_k =\Sigma _{k=2} ^{\infty} a_{k-1} [/itex]

Well, the question is, does the theorem permit all these?

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# Infinite Series question

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