Geometric Series

Series are similar to sequences, except that with series, you determine the sum of terms of the series, not just what the final value will be. There are many different ways to find the sums of series, and one is where the series is in Geometric Series form. Examples are below, along with the forms.

A geometric series is in the form: \[\sum _{n=0}^{\infty }\:c(r^n)\] If |r| < 1 and n = 0, then the sum can be found by evaluating: \[c \over 1-r\] If |r| < 1 and n is not 0, then the sum can be found by evaluating: \[cr^n \over 1-r\] If |r| >= 1, the series is no divergent and there is no sum

Steps:
1. Determine the c, r, and n values
2. Follow the above rules to find the sum if one can be found


Question 1: \[\sum _{n=0}^{\infty }\:(1/3)^n\]

Question 2: \[\sum _{n=0}^{\infty }\:5(2^n)\]

Question 3: \[\sum _{n=2}^{\infty }\: {2(-1^n) \over 8^n}\]