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.
+14 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.
+14 \(\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ...\)
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
