SOLUTION: In the expansion of (1+x)n, two times the coefficient of x5 is equal to the sum of the coefficient of x4 + x6. Find the possible values of n.
2(nC5) = nC4 + nC6 , find n
Algebra.Com
Question 1040101: In the expansion of (1+x)n, two times the coefficient of x5 is equal to the sum of the coefficient of x4 + x6. Find the possible values of n.
2(nC5) = nC4 + nC6 , find n
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
2*(n)(n-1)(n-2)(n-3)(n-4)/5! (the n-5)! cancels the (n-5)! on the bottom
That equals n(n-1)(n-2)(n-3)/4! +n(n-1)(n-2)(n-3(n-4)(n-5)/6!
===========================
I can cancel n(n-1)(n-2)(n-3) from everything, because it is in all terms.
2(n-4)/120=1/24 + (n-4)(n-5)/720
==============================
The first term will be (n-4)/60
Now put everything over a common denominator of 720
12(n-4)=30+(n-4)(n-5), and since they are all over the same number 720, I can remove it without changing the result.
12n-48=30+n^2-9n+20
0=n^2-21n+98
0=(n-14)(n-7)
n=14 or 7
14C5=2002
14C4=1001
14C6=3003
7C5=21
7C4=35
7C6=7
RELATED QUESTIONS
Find the coefficient of x5 in the expansion of (x +... (answered by ewatrrr)
Find the Coefficient of X^n in the expansion of... (answered by KMST)
In the expansion of (2x+1)^n, the coefficient of the x^2 term is 40n , where n is a... (answered by ikleyn)
the coefficient of x^2 in the expansion of (2x+k)^6 is equal to the coefficient of x^5 in (answered by greenestamps)
In the expansion of (1+x)^21,the coefficient of (2r+1)th term is equal to the coefficient (answered by KMST)
Find the coefficient of x^22 in the expansion of... (answered by KMST)
In the expansion of (1-2x)^11 the coefficient of x^3 is k times the coefficient of x^2.... (answered by Boreal)
find the coefficient of x^2 in the expansion of {x -... (answered by greenestamps)
The coefficient of x^2 is 69 in the expansion of (1-ax)^24, where a > 0. Find the... (answered by greenestamps)