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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 $\displaystyle \overbrace{x*x*x*x* .....*x}^{n-times}$. Last edited by MozartInACan; January 5th, 2017 at 09:46 AM. January 5th, 2017, 03:43 PM   #2
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 Originally Posted by MozartInACan 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 $\displaystyle \overbrace{x*x*x*x* .....*x}^{n-times}$.
I assume that (2) is related to (1)

$x^n = (-1)^{n-1}x^n + \displaystyle{\sum_{k=1}^{n-1}}~(-1)^{k-1} \begin{pmatrix}n \\ k \end{pmatrix}x^k$

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 $a = 0$, $\overbrace{x*x*x* \cdots *x}^{n\text{ terms}} = 1 - (1-x)^n$. Last edited by quasi; January 6th, 2017 at 09:06 AM. Tags closed, find, operation, values Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post FightingMongooses Real Analysis 2 June 26th, 2016 06:15 AM Davebungo Calculus 0 January 13th, 2014 02:30 PM 03sqq Real Analysis 4 November 13th, 2012 03:40 AM space55 Calculus 0 October 10th, 2010 03:23 PM sivela Abstract Algebra 1 January 25th, 2010 05:52 AM

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