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June 20th, 2019, 11:28 AM  #1 
Senior Member Joined: Jan 2012 Posts: 140 Thanks: 2  Question related with Binomial Theorem
How can we find the index 'n' of the binomial $\displaystyle \left ( \frac{x}{5}+\frac{2}{5} \right )^{n}$, $\displaystyle n\epsilon N$ if the 9th term of the expansion has numerically the greatest coefficient. Thx. 
June 20th, 2019, 12:59 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,786 Thanks: 708 
The coefficients are $\binom{n}{k}$ for $0\le k\le n$. The maximum is in the middle. If $n$ is even then the max is at $\frac{n}{2}$. If $n$ is odd, it is max at a pair at $\frac{n1}{2}$ and $\frac{n+1}{2}$. You can work it out yourself. Be careful, $k$ starts at $0$. 
June 20th, 2019, 01:07 PM  #3  
Senior Member Joined: Jan 2012 Posts: 140 Thanks: 2  Quote:
Last edited by happy21; June 20th, 2019 at 01:09 PM.  
June 20th, 2019, 03:39 PM  #4  
Senior Member Joined: Sep 2016 From: USA Posts: 635 Thanks: 401 Math Focus: Dynamical systems, analytic function theory, numerics  Quote:
 
June 20th, 2019, 11:34 PM  #5 
Senior Member Joined: Jan 2012 Posts: 140 Thanks: 2  
June 21st, 2019, 12:29 PM  #6 
Global Moderator Joined: May 2007 Posts: 6,786 Thanks: 708  

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