I am having trouble with Riemann sum for a geometric series. The question prompted me to find the area of the region beneath the curve of e^x from x = 0 to x = 1.
Here is what I have so far:
change in x = 1/n
xi = i/n
f(x) = e^x
f(xi ) = e^(i/n)
Area = lim as n goes to infinity of the sum from i = 1 to n of e^(i/n) times 1/n
then, since this is a geometric sequence, it can be simplified to:
Area = lim as n goes to infinity of 1/n * e^(1/n) * (e-1)/(e^(1/n)-1)
i have no clue how to solve this limit. I tried l'Hopital's rule, but got nowhere. Any help is very much appreciated.