We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
158
4
avatar+57 

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+5664 
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+5664 
+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+57 
+2

Thanks!

vindou  Jan 27, 2019

5 Online Users

avatar