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Question 865729: find the sum of infinite geometric series -16+12-9+...
Thank you!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! The first term is -16. So a = -16
The common ratio is 12/(-16) = -3/4. You find this by dividing any term by it's previous term. It helps to keep the common ratio as a fraction. So r = -3/4
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We know a = -16 and r = -3/4. Because |r| < 1 is true, we know that the infinite geometric series converges to some fixed number (and it doesn't diverge).
We find this sum using the formula
S = a/(1 - r)
S = (-16)/(1 - (-3/4)) ... plug in a = -16 and r = -3/4
S = (-16)/(1 + 3/4)
S = (-16)/(4/4 + 3/4)
S = (-16)/(7/4)
S = (-16)*(4/7)
S = -64/7
This means -16+12-9+... = -64/7
Note: -64/7 = -9.14285714285714 approximately, but it's always a better idea to stick to the exact answer. This is because it's easier to get the approximate answer from the exact (it's usually harder to go from approximate to exact).
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