SOLUTION: Find the sum to infinity of the following: 16, 12, 9, 27/4

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Question 1197507: Find the sum to infinity of the following: 16, 12, 9, 27/4
Found 2 solutions by math_helper, MathTherapy:
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
For a geometric series, the n-th partial sum is:


This problem presents a geometric sequence with and .
The infinite sum exists because , and is the limit of as n goes to infinity:
Using "Lim" to denote "Limit as n goes to infinity":
Lim () = Lim ( )

= Lim ( )
= ( 16 * 4 * 1 )
= 64
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Find the sum to infinity of the following: 16, 12, 9, 27/4
This is a GEOMETRIC progression since it has a common ratio (r) of . Furthermore, |r| < 1.
  Sum of an INFINITE GEOMETRIC sequence: 
                                          ----- Substituting 16 for a1, and  for r (common ratio) 
                                         
                                              

Sum of this INFINITE GEOMETRIC series: 16(4) = 64
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