Solved: Closed Form Solution for SIGMA e^(i/n)

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Homework Help Overview

The discussion revolves around finding the closed form value for the summation of e^(i/n) from i=0 to n. The problem is situated within the context of series and exponential functions.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the expansion of the summation and question whether it resembles a geometric series. One participant suggests substituting e^(1/n) with a variable to simplify the expression.

Discussion Status

The discussion is ongoing, with participants sharing initial thoughts and approaches. Some guidance has been offered regarding potential substitutions and the identification of the series type, but no consensus has been reached yet.

Contextual Notes

There is a noted uncertainty regarding the relevant equations and methods for approaching the problem, as participants express a lack of familiarity with similar problems.

Dissonance in E
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Homework Statement



Find the closed form value for

n
SIGMA e^(i/n)
i= 0

Homework Equations



?

The Attempt at a Solution



summation expands to
1 + e^(1/n) + e^(2/n) - - - - - e^1

To be honest i have no clue how to go about these kinds of problems so a general help would be nice.

Thanks
 
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Try writing e^\frac{1}{n} = x, e^\frac{i}{n} = x^i, and see where that leads you.
 
Dissonance in E said:

Homework Statement



Find the closed form value for

n
SIGMA e^(i/n)
i= 0

Homework Equations



?

The Attempt at a Solution



summation expands to
1 + e^(1/n) + e^(2/n) - - - - - e^1

To be honest i have no clue how to go about these kinds of problems so a general help would be nice.

Thanks

Might this be a geometric series?
 
Looks like it to me!
 

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