anonymous
  • anonymous
Find the sum of the infinite geometric series 8 + 4 + 2 + 1 +...
Mathematics
jamiebookeater
  • jamiebookeater
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jim_thompson5910
  • jim_thompson5910
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jim_thompson5910
  • jim_thompson5910
|dw:1433381109007:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1433381124919:dw|

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jim_thompson5910
  • jim_thompson5910
Rule \[\Large \sum_{k=1}^{\infty}a*r^{k-1} = \frac{a}{1-r}\] if and only if |r| < 1. Since r = 0.5, that makes |r| < 1 true, which allows us to use the formula
anonymous
  • anonymous
I'm confused, do I used that equation to find the sum? If so what is a?
jim_thompson5910
  • jim_thompson5910
I posted what 'a' was in my second post above
jim_thompson5910
  • jim_thompson5910
a = first term
jim_thompson5910
  • jim_thompson5910
a = 8 is the first term r = 0.5 is the common ratio you use \[\Large S = \frac{a}{1-r}\]
anonymous
  • anonymous
So the sum is 16?
geerky42
  • geerky42
Yes.
jim_thompson5910
  • jim_thompson5910
yep S = 16

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