Assignment 2 answer key
1. Determine which of the following series is divergent and explain why.
Solution: We will use the statement that if limn an = 0 then series
n=1 an is divergent.
a)
n=1
b)
n=1
n+1
1
n+1
; lim
= = 0. The series diverges.
2n 1 n 2n +
Continuous Compounding
This process of compounding repeatedly has a limit at n ! 1. This is called continuous
compounding. Lets nd this formula: we will do it for t = 1.
r n
A = lim P 1 +
n!1
n
r n
= P lim 1 +
n!1
n
If we let x = r/n, then n = r/x. Then a