+0

0
52
4

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
+14
0

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
0

Guest Aug 10, 2022
#3
+14
0

$$\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ...$$

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
0

:D        thankss

Guest Aug 10, 2022