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wcaprar
 3 years ago
What is the sum of the infinite series?
wcaprar
 3 years ago
What is the sum of the infinite series?

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wcaprar
 3 years ago
Best ResponseYou've already chosen the best response.1\[\sum_{n=2}^{\infty} 2^n/3*5^{n+2}\]

wcaprar
 3 years ago
Best ResponseYou've already chosen the best response.1I see that you can take out the 5^2 and multiply that with three then simplify to get \[(1/75)*(2/5)^n\] which is a geometric series. But when I solve it out like you would a regular geometric series I get 1/45. But wolframalpha says 20

joemath314159
 3 years ago
Best ResponseYou've already chosen the best response.1your idea is correct. lets make sure the arithmetic is correct

joemath314159
 3 years ago
Best ResponseYou've already chosen the best response.1\[\frac{1}{75}\sum_{n=2}^{\infty}\left(\frac{2}{5}\right)^n=\frac{1}{75}\left(\frac{\frac{4}{625}}{1\frac{2}{5}}\right)\]

wcaprar
 3 years ago
Best ResponseYou've already chosen the best response.1How do you get 4/625 on top?

joemath314159
 3 years ago
Best ResponseYou've already chosen the best response.1we are starting at n=2, not n=1. The first term of the sequence is 4/625.
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