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

Answer 1

S = 9/(1-r)

If r>=0, you can see that 9/1=9 would be the smallest possible sum, if r=0. That is, if the sequence is
9 0 0 0 0 0 ......

Any other value for r will produce nonzero terms, and therefore a larger sum.

You can investigate what happens when r < 0.