SOLUTION: Find the sum of the infinite geometric series 3+2+4/3+8/9+.....

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Question 71383This question is from textbook Advanced Algebra
: Find the sum of the infinite geometric series 3+2+4/3+8/9+..... This question is from textbook Advanced Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First we need to find the nth term of the series, or in other words the general formula. To go from 3 to 2, multiply by 2/3, and to go from 2 to 4/3 again you must multiply by 2/3. So the geometric ratio r is 2/3 and since the sequence starts at 3, the initial term a=3. So using the infinite sum formula we get
S=a%2F%281-r%29Note: r<0 for an infinite sum to converge
S=3%2F%281-2%2F3%29
S=3%2F1%2F3
S=9
So as the sum of the infinite series is 9.