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January 5th, 2017, 09:23 AM  #1 
Newbie Joined: Jan 2017 From: Nowhere Posts: 5 Thanks: 1  Find the values of a so that the operation is closed in [0;1]
I would appreciate anyone's contribution for the following exercises : 1)Find the values of a so that the operation $\displaystyle x * y = x + y  xy  ax  ay +a $ is stable in the set [0;1] //// First one was solved 2) For a=0, find a formula for $\displaystyle \overbrace{x*x*x*x* .....*x}^{ntimes} $. Last edited by MozartInACan; January 5th, 2017 at 09:46 AM. 
January 5th, 2017, 03:43 PM  #2  
Senior Member Joined: Sep 2015 From: USA Posts: 2,552 Thanks: 1402  Quote:
$x^n = (1)^{n1}x^n + \displaystyle{\sum_{k=1}^{n1}}~(1)^{k1} \begin{pmatrix}n \\ k \end{pmatrix}x^k$ I leave it to you to prove this via induction.  
January 6th, 2017, 08:57 AM  #3 
Member Joined: Dec 2016 From: USA Posts: 46 Thanks: 11 
When $a = 0$, $\overbrace{x*x*x* \cdots *x}^{n\text{ terms}} = 1  (1x)^n$. Last edited by quasi; January 6th, 2017 at 09:06 AM. 

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