June 15th, 2018, 12:05 AM  #1 
Member Joined: Aug 2017 From: India Posts: 42 Thanks: 1  Failing to understand the problem
I am failing to understand the problem to make any attempt. How to solve it ? and what is the significance of these kind of problems?

June 15th, 2018, 07:37 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,191 Thanks: 1649 
Consider the consequences of x$_1$ = 0.

June 15th, 2018, 08:43 AM  #3 
Senior Member Joined: Sep 2015 From: USA Posts: 2,011 Thanks: 1044 
for (a) consider $x_1 = 2$ for (b) consider values where $x = \dfrac{1}{x1}$ for (c) count how many solutions there are to the equation mentioned for (b) for (d), suppose there was a set of $x_k$ such that the product equalled $0$. well clearly one of the $x_k=0$. It can only be the 20007th value or we're going to try and divide by $0$ to find $x_{k+1}$ But there is no value $x$ such that $\dfrac{1}{x1}=0$ and thus there is no way for the recursion to produce $x_{2007}=0$ 
June 15th, 2018, 09:04 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 19,191 Thanks: 1649  
June 15th, 2018, 09:09 AM  #5  
Senior Member Joined: Sep 2015 From: USA Posts: 2,011 Thanks: 1044  Quote:
Actually it's completely wrong. Let $x_1=0$ The resulting sequence is derived without complication and the product does equal 0. Last edited by romsek; June 15th, 2018 at 09:12 AM.  
June 15th, 2018, 09:58 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 19,191 Thanks: 1649 
The product doesn't include x$_1$, so it isn't zero.

June 15th, 2018, 10:47 PM  #7 
Member Joined: Aug 2017 From: India Posts: 42 Thanks: 1 
Thank you very much. From your support, I finally arrived like this A. $\displaystyle x1 = 2, x2 = 1 (2,1), x1=1, \text{ Invalid Condition} $ B. Solving for $\displaystyle x = 1/(x1); $ $\displaystyle x = (1 \pm \sqrt{5})/2 $ C. There are only two choices for x as above in B. D. There does not exist a choice. Last edited by skipjack; June 16th, 2018 at 12:47 AM. 
June 16th, 2018, 12:52 AM  #8 
Global Moderator Joined: Dec 2006 Posts: 19,191 Thanks: 1649 
Your answer for (A) is expressed unclearly. What about (E)? 
June 16th, 2018, 01:03 AM  #9 
Member Joined: Aug 2017 From: India Posts: 42 Thanks: 1  
June 16th, 2018, 01:52 AM  #10 
Global Moderator Joined: Dec 2006 Posts: 19,191 Thanks: 1649 
(A) specifies x$_1$ is not equal to 1. However, (A) is incorrect.


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