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anonymous
 3 years ago
how to find the sum of this?
anonymous
 3 years ago
how to find the sum of this?

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\sum_{k=1}^{\infty}\left( 2^{k}+5^{k+1} \right)\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0break in to two parts and add

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0first one is \[\sum_{k=1}^{\infty}\frac{1}{2^k}=1\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0how did you find that? (Haven't done this in a long time)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0the sum is 9/4 (after wolframalpha) but I don't know how to find it

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0the first term is a geometric series with first term 1/2 and ratio 1/2, the second term is a geometric series with first term 1 and ratio 1/5 use the formula \[S=\frac{ a_1 }{ 1r }\] to find the sum of an infinite geometric series

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so then it is s =0.5/(10.5)=1 and 1/(11/5)=5/4 1+5/4 =9/4
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