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irinina [24]
3 years ago
5

Use the formula to evaluate the infinite series. Round your answer to the nearest hundredth if necessary. 72 + 12 + 2 + . . . Fo

rmula for a converging infinite series. a1 is the first term and r is the common ratio. 86.4 14.4 6 432
Mathematics
1 answer:
____ [38]3 years ago
6 0
The first term is a = 72

The common ratio is r = 1/6.
We multiply each term by 1/6, which is the same as dividing each term by 6.
To find r, divide any term you want over the previous term
r = 12/72 = 1/6
r = 2/12 = 1/6
etc.

Now use the infinite sum formula to find S
S = infinite sum
S = a/(1-r) ... see note below
S = 72/(1-1/6)
S = 72/(6/6 - 1/6)
S = 72/(5/6)
S = (72/1) divided by (5/6)
S = (72/1)*(6/5)
S = (72*6)/(1*5)
S = 432/5
S = 86.4

Answer: 86.4

note: this infinite sum formula only works if -1 < r < 1. In the case of r = 1/6 = 0.167 (approx), this r value is between -1 and 1. 
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3 years ago
<img src="https://tex.z-dn.net/?f=5%20%5Ctimes%20%5Cfrac%7B1%7D%7B2%7D%20" id="TexFormula1" title="5 \times \frac{1}{2} " alt="5
lidiya [134]
5 x 1/2

decimal form :
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fraction form : 2 1/2
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Read 2 more answers
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