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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?

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+941

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

Thanks so much!

AnonymousConfusedGuy  Jan 17, 2018
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#1
+85866
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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

CPhill  Jan 17, 2018
#2
+941
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Thanks!

AnonymousConfusedGuy  Jan 17, 2018

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