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What is the smallest integer that can possibly be the sum of an infinite geometric series whose first term is 13?

 Oct 23, 2022
 #1
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The answer is -13.

 Oct 23, 2022
 #2
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This needs to be minimized: \({13\over 1-r}\).

 

Where -1 < r < 1. (If that isn't true then the series doesn't really have a sum)

 

If r is -1, the sum is 13/2 = 6.5. Rounding this figure up will both give an integer and put r back into its accepted range, so the smallest integer that can possibly be the sum of an infinite geometric series whose first term is 13 is 7. (the common ratio would be -6/7)

 Oct 23, 2022

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