# S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
 It is currently Wed, 19 Jun 2013 05:15:04 UTC

 All times are UTC [ DST ]

 Page 1 of 1 [ 7 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: Binomial TheoremPosted: Mon, 13 Sep 2010 02:51:35 UTC

Joined: Mon, 13 Sep 2010 02:43:18 UTC
Posts: 9
Location: Malaysia
In the expansion of (1+x)^n, the coefficient of x^9 is the arithmetic mean of the coefficient of x^8 and x^10. Find the possible values of n where it is a positive integer.

Is it possible to do it manually instead of using a tables book?

Top

 Post subject: Posted: Mon, 13 Sep 2010 14:27:37 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12169
Location: Austin, TX
Binomial Theorem

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Posted: Tue, 14 Sep 2010 06:18:49 UTC
 S.O.S. Oldtimer

Joined: Fri, 27 Jul 2007 10:17:26 UTC
Posts: 278
Location: Chandler, AZ, USA
Yes it is - you have to set nC9 = (nC8 + nC10)/2 and solve for n.
This equation, when you apply the definition of nCr (binomial theorem), leads to a quadratic in n with two integer solutions. You will have to be adept at simplifying with factorials, but the solutions are relatively small integers. Good luck!

Spoiler:
Quadratic is , and the solutions are .

Top

 Post subject: Posted: Tue, 14 Sep 2010 07:55:26 UTC
 Moderator

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6066
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
alstat wrote:
Yes it is - you have to set nC9 = (nC8 + nC10)/2 and solve for n.
This equation, when you apply the definition of nCr (binomial theorem), leads to a quadratic in n with two integer solutions. You will have to be adept at simplifying with factorials, but the solutions are relatively small integers. Good luck!

Spoiler:
Quadratic is , and the solutions are .

Sorry but you missed out another 8 possibile values of n.

_________________

Top

 Post subject: Posted: Wed, 15 Sep 2010 00:16:00 UTC
 S.O.S. Oldtimer

Joined: Fri, 27 Jul 2007 10:17:26 UTC
Posts: 278
Location: Chandler, AZ, USA
outermeasure wrote:
alstat wrote:
Yes it is - you have to set nC9 = (nC8 + nC10)/2 and solve for n.
This equation, when you apply the definition of nCr (binomial theorem), leads to a quadratic in n with two integer solutions. You will have to be adept at simplifying with factorials, but the solutions are relatively small integers. Good luck!

Spoiler:
Quadratic is , and the solutions are .

Sorry but you missed out another 8 possibile values of n.

Are you refering to the trivial coefficients of zero for n less than 8? That's "clever" - I did miss them, but there are only 7, as n is to be positive. What would be the 8th "other solution" and what method is needed to find it?

Of course one could argue that a coefficient of zero really means the poynomial doesn't actually HAVE that term!

Top

 Post subject: Posted: Mon, 20 Sep 2010 05:05:05 UTC

Joined: Mon, 13 Sep 2010 02:43:18 UTC
Posts: 9
Location: Malaysia
alstat wrote:
Yes it is - you have to set nC9 = (nC8 + nC10)/2 and solve for n.

is nc9 = n(n-1)(n-2)(n-3)(n-4)....(n-8)? If so, how do I simplify them (including nC8 and nC10) ?

Top

 Post subject: Posted: Tue, 21 Sep 2010 06:50:21 UTC
 S.O.S. Oldtimer

Joined: Fri, 27 Jul 2007 10:17:26 UTC
Posts: 278
Location: Chandler, AZ, USA
nCr = n!/[r!(n-r)!]

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 7 posts ]

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous