Question 305226: How do you find the sum of infinite geometric series?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! How do you find the sum of infinite geometric series?
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S(n) = a + ar + ar^2 +...+ar^(n-1)
r*S(n) = ar + ar^2 + ..+ar^(n-1)+ ar^n
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Subtract the 2nd line from the 1st to get:
S(n) - r*S(n) = a -ar^n
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Factor both sides and solve for S(n):
S(n)*(1-r) = a(1-r^n)
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S(n) = [a(1-r^n)/(1-r)
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If 0< r < 1 and n goes to infinity, r^n goes to zero
and you get:
S(n) = a/(1-r)
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Cheers,
Stan H.
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