SOLUTION: discuss how you will find the sum of the series:
1/2 + 1/4 + 1/8+ ... + 1/512
* our topic focuses on harmonic and fibonacci sequence but it can be other types of sequences o
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-> SOLUTION: discuss how you will find the sum of the series:
1/2 + 1/4 + 1/8+ ... + 1/512
* our topic focuses on harmonic and fibonacci sequence but it can be other types of sequences o
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Question 1120744: discuss how you will find the sum of the series:
1/2 + 1/4 + 1/8+ ... + 1/512
* our topic focuses on harmonic and fibonacci sequence but it can be other types of sequences or series :-) Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! a geometric series is defined as
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x(n) = a * r^(n-1), where x(n) is the nth term, r is the common ratio and a is the first term
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for this problem a = 1/2 and r = 1/2
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the sum of the first n terms of a geometric series is defined as
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summation for k from 0 to n-1 of (ar^k) = a * (1 - r^n) / (1 -r) =
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(1/2) * (1 -(1/2)^n) / (1 -(1/2)) =
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(1/2) * (1 -(1/2)^n) * 2 = (1 -(1/2)^n)
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