How do you find the sum of the infinite geometric series 3 – 12 + 48 – 192 + …?

Answer 1

The sum of this series is undefined (it alternates tending towards #+oo# and #-oo#)

The sum of an infinite geometric series only exists if the geometric ratio, #r# is such that #abs(r) < 1#
In this case the geometric ratio is #(-12)/3=-4# so the series does not converge and the sum is undefined.
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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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