1. The problem statement, all variables and given/known data Determine the limit of the sequence: an = (1+(5/n))2n 2. Relevant equations L'hopitals rule, or at least that's what I'm thinking. Otherwise, general formulas for determining the limit of a sequence. 3. The attempt at a solution an = (1+(5/n))2n Considering the behavior of the sequence as n goes toward infinity, (5/n) is a very small change in size, so it goes approximately to zero, leaving: an = (1)2n Which, as n goes to infinity, is essentially: 1∞, an indeterminate form. To resolve this, take the natural log: an = ln(12n) = 2n(ln(1)) Rearranging it to give a L'hopital's rule acceptable form of 0/0, gives: ln(1)/[1/2n] And taking the derivative: 0/(-1/2n2) = 0 And raising to e to get back to the original value: e0 = 1 Except this is clearly incorrect, as we determined in class that the sequence converted to something around 22,000, and not 1. Other than this, I tried not canceling the (5/n), taking the log, and then splitting it using the limit law: lim[f(x)*g(x)] = lim(f(x)) * lim(g(x)) But this didn't work either, as the limit of 2n by itself diverges as n goes to infinity, and this sequence is known not to diverge.