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What is the smallest integer that can possibly be the sum of an infinite geometric series whose first term is 9?

 

 

Thanks so much!

 Jan 17, 2018
 #1
avatar+101898 
+1

Note that  we are trying to minimze this sum  for   some value of r

 

S =   9 / (1 - r)  

 

If   r  =  -1/2       the sum  is 6

If r  =   -4/5        the sum is  5

If r  = -5/4          the sum is  4

 

But    l r  l    must be  <  1  ......so  r  =  -5/4  isn't allowed

 

So.....it appears that the sum is minimized  to an integer whenever  r  =  -4/5   and the minimized sum is  5

 

 

cool cool cool

 Jan 17, 2018
 #2
avatar+1438 
+1

Thanks!

AnonymousConfusedGuy  Jan 17, 2018

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