Calculating the Sum of Infinite Series: 2^k/k! Method

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Homework Help Overview

The discussion revolves around finding the sum of the infinite series represented by 2^k/k!. Participants explore the nature of the series and its relation to known mathematical concepts.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants consider the Taylor expansion of e^x as a potential approach, questioning its applicability to the series in question. There is some confusion regarding the classification of the series as a power series.

Discussion Status

The conversation has evolved with participants clarifying their thoughts and confirming the relevance of the Taylor series for e^2. There appears to be a productive direction as they reconcile their understanding of the series and its closed form.

Contextual Notes

Some participants express uncertainty about the nature of the series and its classification, which may impact their approach to finding the sum.

apiwowar
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how would i go about finding the sum of the infinite series 2^k/k!?

its not a geometric so i can't use the formulas for that so i really have no clue.

any help would be appreciated
 
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It might help to know the taylor expansion of e^x.
 
i was thinking that but could that work since that's not a power series?
 
apiwowar said:
i was thinking that but could that work since that's not a power series?

The taylor expansion of e^x IS a power series. It's not geometric, I'm not sure what you are worried about.
 
wait nevermind, i was confusing myself.
so what I am talking about would be the closed form for the taylor series e^2 then, right?
 
apiwowar said:
wait nevermind, i was confusing myself.
so what I am talking about would be the closed form for the taylor series e^2 then, right?

I don't see anything wrong with that.
 
thanks
 

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