+0  
 
0
37
4
avatar+53 

If \(k = \frac{1}{1+2x}\), 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.

 Jan 27, 2019
 #1
avatar+3976 
0

xxxx

 Jan 27, 2019
edited by Rom  Jan 27, 2019
edited by Rom  Jan 27, 2019
 #2
avatar
+2

Rom: I got different result!!:

 

k =(0.2, 0.04, 0.008, 0.0016, 0.00032, 0.00006 4, 0.00001 28, 0.00000 256, 0.00000 0512, 0.00000 01024.....to infinity)

x = (2, 12, 62, 312, 1 562, 7 812, 39 062, 195 312, 976 562, 4 882 812......to infinity)
k = ∑[1/(1+2*(5^n - 1)/2), n, 1,∞] = 1/4

 Jan 27, 2019
edited by Guest  Jan 27, 2019
edited by Guest  Jan 27, 2019
 #3
avatar+3976 
+2

you're right!

my method is messed up.  Thanks

 

The sum is actually just

 

\(\sum \limits_{i=1}^\infty \dfrac{1}{5^i} = \dfrac{1}{1-\dfrac 1 5}-1=\dfrac 5 4 - 1 = \dfrac 1 4\)

Rom  Jan 27, 2019
edited by Rom  Jan 27, 2019
edited by Rom  Jan 27, 2019
 #4
avatar+53 
+2

Thanks!

vindou  Jan 27, 2019

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