# Maths

Can the sum of an infinite geometric sequence be negative?

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1. certainly
S = a/(1-r)
so, if a<0, S<0

extra credit: why cannot (1-r) be negative?

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2. oobleck:
can you swap 1-r with r-1 if the common ratio is greater than one? In a question I was doing, the markscheme used r-1 and the sum was positive, but if you use 1-r the answer would be negative. Does it matter?

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3. the problem is, that if 1-r < 0 then r > 1 and the series will not converge.
The formula still works for a finite number of terms, however.

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