Limit of Riemann Sums with Infinite Terms: Help Needed

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Homework Help Overview

The discussion revolves around evaluating the limit of a Riemann sum involving exponential functions as the number of terms approaches infinity. The problem is situated within the context of calculus, specifically focusing on the concepts of limits and Riemann sums.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to evaluate the limit of a sum involving exponential terms but expresses uncertainty about the evaluation process. Some participants suggest considering the series as a geometric series and computing the sum, while others propose examining the function f(x) = e^x over a specific interval and analyzing upper and lower sums.

Discussion Status

The discussion includes various approaches to the problem, with some participants providing guidance on how to interpret the sum and suggesting methods to analyze it. The original poster indicates they have resolved the issue, but the conversation reflects a range of interpretations and suggestions without a definitive consensus.

Contextual Notes

The original poster expresses uncertainty about whether the question was posted in the correct forum, indicating a potential concern about the appropriateness of the discussion context.

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Homework Statement


[tex]\underset{n\rightarrow\infty}{lim}\frac{e^{1/n}+e^{2/n}+e^{3/n}+\cdots+e^{n/n}}{n}[/tex]

The Attempt at a Solution



done something with Riemann sums however didn't get far, other than that I'm not to sure how to evaluate this. any help would be great, thanks (also not sure if i posted in the right place, if i didnt soz.)
 
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The top looks like a geometric series; please try computing the sum and see if it works.
 
Consider f(x) = e^x on the interval [0,1]. Partition [0,1] into n equal subintervals and look at the upper and lower sums.
 
Solved it thanks a lot.
 

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