How do you find the sum of the geometric series #8+4+2+1+…#?

Answer 1

The sum of a convergent geometric series #sum_{n=0}^{infty}ar^n# is #frac{a}{1-r}#. Since #a=8# and #r=1/2# in the posted geometric series, the sum is #frac{8}{1-frac{1}{2}}=16#.

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Answer 2

Emma Aldridge

To find the sum of the geometric series (8+4+2+1+\ldots), you need to identify the common ratio (r) between consecutive terms. In this series, each term is half of the previous term. So, the common ratio (r) is (0.5). The formula to find the sum of an infinite geometric series is (S = \frac{a}{1 - r}), where (S) is the sum, (a) is the first term, and (r) is the common ratio. Substituting the values, (a = 8) and (r = 0.5), into the formula gives (S = \frac{8}{1 - 0.5} = \frac{8}{0.5} = 16). Therefore, the sum of the series (8+4+2+1+\ldots) is (16).

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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.