Download Solutions for Warm Up Quiz on Infinite Sequences

Solutions for Warm Up Quiz on Infinite Sequences
1. Briefly, explain the difference between an Infinite Series and a Infinite
Sequence?
An Infinite Series is an infinite summation of a list of numbers ordered in a
1 1 1 1
1
specific way. Example: + + + + ...+ n + ...
1 2 4 8
2
A Sequence, an , is a list of numbers written in an explicit order.
Example: 1,1,2, 3,5,8,..., This is the Fibonacci sequence, but it could be as simple
as 1, 2, 3, 4, …, the natural numbers.
2. Briefly, explain the difference between an Arithmetic Sequence and a
Geometric Sequence.
An Arithmetic Sequence is a sequence in which any 2 consecutive sequences
differ by a constant, d. For example, the even numbers, 2, 4, 6, 8, …, the constant
d = 2.
A Geometric Sequence is a sequence in which the quotient of any number in the
sequence divided by the previous number is constant, r.
1 1 1 1
For example: 1, , , , ,... , where r = 1/2
2 4 8 16
3. What is the notation used for sequence? You enclose the sequence in curly
brackets, for example: { an }
4. What is the domain of a sequence? The domain of a sequence is a subset of the
positive integers. If the domain is finite or infinite, depending on whether the
sequence is finite or infinite, respectively.
5. Determine whether the following sequence converges or diverges. If it
converges, find its limit.
2n -1
2n
1
ì 2n -1 ü
Þ lim í
- lim Þ 2 - 0 = 2 , Therefore it converges
ý Þ lim
x®¥
x®¥
x®¥
n
n
n
î n þ
and the limit is 2.
an =