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
Algebra.Com
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
:
x(n) = a * r^(n-1), where x(n) is the nth term, r is the common ratio and a is the first term
:
for this problem a = 1/2 and r = 1/2
:
the sum of the first n terms of a geometric series is defined as
:
summation for k from 0 to n-1 of (ar^k) = a * (1 - r^n) / (1 -r) =
:
(1/2) * (1 -(1/2)^n) / (1 -(1/2)) =
:
(1/2) * (1 -(1/2)^n) * 2 = (1 -(1/2)^n)
:
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