Limit of sum of exponential terms as n approaches infinity

[adriang]

Homework Statement

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

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.)

 

[╔(σ_σ)╝]

The top looks like a geometric series; please try computing the sum and see if it works.

 

[snipez90]

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.

 

[adriang]

Solved it thanks a lot.