Let where and
for n in naturals
Find the limit of Hint: One upper bound of the sequence is
The ACTUAL fact us that ...the sum is infinite, and either one defines the number e that way, or else defines some other way and proves the above sum is e. Anyway, any decent calculus book must include a discussion on this. For example, Apostol's "Calculus I" has several interesting parts on the number e, including its definition as that number x for which .