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If k = 1/(1+2x), where x is an integer greater than 1 and k can be represented as a terminating decimal, find the sum of all possible values of k.

 Aug 10, 2022
 #1
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To figure out whether a fraction is a terminating decimal, the denominator of the fraction must be a power of 2 and/or 5 ONLY. We know 1+ 2x won't be a multiple of 2 as x is an integer. We can however express the denominators as powers of 5.

 

So all we have to find is:

 

\(\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ...\)

 

If you need more help, respond to this answer I guess.

 Aug 10, 2022
 #2
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yes please

Guest Aug 10, 2022
 #3
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\(\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ...\)

 

The expression above can be determined as the sum of an infinite geometric series

 

Each term can be written as \(1*(\frac{1}{5})^n\)

 

Using this information, we can plug the values into the formula for the sum of an infinite geometric series

\(\frac{\frac{1}{5}}{1 - \frac{1}{5}} = \frac{1}{4}\)

 

Finally we get an answer of 1/4

:D

 Aug 10, 2022
 #4
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:D        thankss

Guest Aug 10, 2022

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