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

#1**+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

CPhill
Jan 17, 2018