Sarah M.

asked • 05/05/17

Determine whether the infinite geometric series is convergent or divergent. find its sum.

Determine whether the infinite geometric series is convergent or divergent. If it is convergent, find
its sum. (If the series is divergent, enter DIVERGENT.)
 
1+8/5+(8/5)2+(8/5)3+...

Mark M.

An infinite geometric series is convergent if and only if |r| < 1
What is the common ratio here?
Is the series convergent?
Report

05/05/17

Sarah M.

I don't know the common ratio 
can you please explain
 
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05/05/17

Patrick D.

Hello again Sarah:
 
  In a nutshell.....
  The geometric series will converge to a sum if the fraction in the parenthesis is less than 1 in absolute value.
   
  The series you describe In this problem, the fraction is BIGGER than one, so the series will diverge. The sum grows infinitely large without bound.  Your best answer is DIVERGENT, and the sum is infinite.
 
 Let's look at another example:  SUM [ (1/2)^n ]  , n=0,1,2,3,....infinity
 
    Here the common ratio is 1/2, which is less than one. The theorem states that the sum will converge
     to   1/ (1-1/2) = 1/(1/2) = 2.
 
  so the partial sums : 1 + 1/2 + 1/4 + 1/8 + 1/16 + ...... +   (1/2)^n  will approach 2  as  n --> infinity
 
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05/06/17

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