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anonymous
 one year ago
What do I do, I am unsure how to interpret it as a geometric series.
http://i.imgur.com/pyZd2ip.png
Thanks
anonymous
 one year ago
What do I do, I am unsure how to interpret it as a geometric series. http://i.imgur.com/pyZd2ip.png Thanks

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Empty
 one year ago
Best ResponseYou've already chosen the best response.1You can make a substitution to make it easier perhaps? \[x=(1+c)^{1}\] \[\sum_{n=1}^\infty x^n =8\]

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0I agree with @empty. You can then use the infinite series formula for geometric series to get a value for x. Then solve for c after. That is, 1/(1x) = 8 solve for x. You will get x = something. Then, x = 1/(1+c) so, something = 1/(1+c) solve for c.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Let \(x = 1+c\) Partial sum is\[s_n = x^{1} + x^{2} + x^{=3} + ... + x^{n}\]Multiply both sides by \(x\)\[xs_n = 1 + x^{1} + x^{2} + ... + x^{n+1}\]Subtract 1st equation from 2nd equation\[(x1)s^n = 1 + x^{n}\]\[s_n = \frac{ 1 + x^{n} }{ x1 }\]Sum of infinite series is\[\lim_{n \rightarrow \infty} s_n = \lim_{n \rightarrow \infty} \frac{ 1 + x^{n} }{ x1 } = 8\]\[\frac{ 1 }{ x1 } = 8\]Solve for \(x\) and then for \(c\).
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