46 783
Assignments Done
Successfully Done
In March 2017
Your physics homework can be a real challenge, and the due date can be really close — feel free to use our assistance and get the desired result.
Be sure that math assignments completed by our experts will be error-free and done according to your instructions specified in the submitted order form.
Our experts will gladly share their knowledge and help you with programming homework. Keep up with the world’s newest programming trends.

Answer on Discrete Mathematics Question for sonam

Question #2114
Use induction to prove that x(2n-1)+y(2n-1) is divisible by x+y for n is the element of natural numbers
Expert's answer
For n =1:

<img src="/cgi-bin/mimetex.cgi?x%5E%7B2n-1%7D+y%5E%7B2n-1%7D%20=%20x+y" title="x^{2n-1}+y^{2n-1} = x+y">& - the condition is satisfied.

Let's assume that <img src="http://latex.codecogs.com/gif.latex?x%5E%7B2n-1%7D+y%5E%7B2n-1%7D" title="x^{2n-1}+y^{2n-1}">
is divisible by (x+y), let's prove it for n+1:

<img src="http://latex.codecogs.com/gif.latex?x%5E%7B2%28n+1%29-1%7D+y%5E%7B2%28n+1%29-1%7D%20=%20x%5E2x%5E%7B2n-1%7D+y%5E2y%5E%7B2n-1%7D%20=%20x%5E2x%5E%7B2n-1%7D+%28y%5E2%20+%20x%5E2%20-%20x%5E2%29y%5E%7B2n-1%7D=%5C%5C%20=x%5E2%28x%5E%7B2n-1%7D+y%5E%7B2n-1%7D%29%20+%28x+y%29%28x-y%29y%5E%7B2n-1%7D" title="x^{2(n+1)-1}+y^{2(n+1)-1} = x^2x^{2n-1}+y^2y^{2n-1} = x^2x^{2n-1}+(y^2 + x^2 - x^2)y^{2n-1}=\\ =x^2(x^{2n-1}+y^{2n-1}) +(x+y)(x-y)y^{2n-1}">
The first term is divisible by assumption and it's shown that the second term is divisible by (x+y) too.
tip Your question requires fast and guaranteed response?   Please   SUBMIT IT


No comments. Be first!

Leave a comment

Ask Your question