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Consider the infinite geometric series
a. Write the first four terms of the series.
b. Does the series diverge or converge?
c. If the series has a sum, find the sum.
 one year ago
 one year ago
Consider the infinite geometric series a. Write the first four terms of the series. b. Does the series diverge or converge? c. If the series has a sum, find the sum.
 one year ago
 one year ago

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Pologirl19Best ResponseYou've already chosen the best response.0
\[\sum_{x=1}^{\infty}4\frac{ 1 }{ 3 }^{x1}\]
 one year ago

tkhunnyBest ResponseYou've already chosen the best response.1
It's a geometric series with r < 1. It converges and the sum is well known. \(4 (1 + 1/3 + 1/9 + 1/27 + ...) = \dfrac{4}{1(1/3)}\) Try not to struggle over ones like this.
 one year ago

Pologirl19Best ResponseYou've already chosen the best response.0
wait were do you get 1/9 and 1/27. Because I got b. it converges and c. it is 6. But I have to show my work. @tkhunny
 one year ago

Pologirl19Best ResponseYou've already chosen the best response.0
Because I I know the formula. it is \[S=\frac{ a1 }{ 1r }\]
 one year ago

tkhunnyBest ResponseYou've already chosen the best response.1
\(\sum\limits_{x=1}^{\infty} 4\left(\dfrac{1}{3}\right)^{x1} = 4\sum\limits_{x=1}^{\infty} \left(\dfrac{1}{3}\right)^{x1} = 4\left(\left(\dfrac{1}{3}\right)^{11} + \left(\dfrac{1}{3}\right)^{21} + \left(\dfrac{1}{3}\right)^{31} + ...\right)\) Are you yet seeing it?
 one year ago

Pologirl19Best ResponseYou've already chosen the best response.0
Ah thank you so much I was really confused. except for I don't get a.
 one year ago

tkhunnyBest ResponseYou've already chosen the best response.1
(1/3)^(11) = (1/3)^0 = 1 4 * 1 = 4 = a1
 one year ago

tkhunnyBest ResponseYou've already chosen the best response.1
a1 is the first term in the series. 4 in this case.
 one year ago

Pologirl19Best ResponseYou've already chosen the best response.0
Wait still a little confused thats only one though
 one year ago

tkhunnyBest ResponseYou've already chosen the best response.1
a is the first term. 4 Use x = 1 in the summation formula. r is the common ratio. 1/3 Just read it from the summation formula. \(\dfrac{4}{11/3} = \dfrac{4}{2/3}\) You're not going to make me do ALL the work, are you?
 one year ago

Pologirl19Best ResponseYou've already chosen the best response.0
No sorry. So it would be 4, 1/3, 1 and infinity. Right
 one year ago

tkhunnyBest ResponseYou've already chosen the best response.1
What would be 4? What would be 1/3? What would be 1? What would be "infinity"? Its an infinite series. Its first term is 4 Its common ration is 1/3 That is ALL the required information to find the sum.
 one year ago

Pologirl19Best ResponseYou've already chosen the best response.0
Well it says write the first four terms of the series
 one year ago

tkhunnyBest ResponseYou've already chosen the best response.1
Then do that. Substitute x = 1, 2, 3, 4. All should be negative. All should be finite.
 one year ago
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