What is the sum of the infinite geometric serie ¾–⁹/16+ 27/64–81/256+...?
1 answer:
9514 1404 393
Answer:
3/7
Step-by-step explanation:
The sum of a geometric series with first term a1 and common ratio r is ...
S = a1/(1 -r)
For a1 = 3/4 and r = -3/4, the sum is ...
S = (3/4)/(1 -(-3/4)) = (3/4)/(7/4) = 3/7
The sum of the series is 3/7.
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<em>Additional comment</em>
The terms rapidly decrease in value, so it doesn't take very many terms for the sum to reach the limit of precision available in most calculators. 100 terms are sufficient to give the sum to 12 significant digits.
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