### A2M3L29-SB-Geometric Series and Summation Notation.notebook

```A2M3L29­SB­Geometric Series and Summation Notation.notebook
Summation Notation
ending "n" value
March 17, 2016
r
n
and starting "n" value
n=1
Geometric Series
Write the sum without using summation notation, and find the sum.
4
n
n=1
= 1+2+3+4
A2M3L29­SB­Geometric Series and Summation Notation.notebook
Write the sum without using summation notation, and find the sum.
March 17, 2016
Let a, ar, ar2,ar3, ar4,, ... be a geometric sequence with the first term a and common ratio r.
Let Sn= a + ar + ar2 + ar3 +.... +ar n­1 be the sum of the first n terms of the geometric series. Sn= a + ar + ar2 + ar3 +.... +ar n­1 r Sn= ar + ar2 + ar3 +.... +ar n
Sn­ r Sn = a ­ ar n
_
Sn(1­r) = a ­ ar n
Sn =
a­ar n
1­r
Use the formula to find the sum of the following series:
Sn =
a­ar n
1­r
where Sn is the sum of the first n terms
of a geometric series 1+2+4+8+16+32+64
A2M3L29­SB­Geometric Series and Summation Notation.notebook
Use the formula to find the sum of the following series:
Evaluate using the formula for the sum of a geometric series. March 17, 2016
Find the sum of the first 12 terms of a geometric and series where A2M3L29­SB­Geometric Series and Summation Notation.notebook
You deposit \$2500 at the beginning of each year for 5 years in an account that pays 3% interest compounded annually. What is the total value of your account at the end of the fifth year? March 17, 2016
Homework: Worksheet
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