In the expansion of (x+y)^n the coefficient of x^4y^(n-4) is 3,876 and the coefficient of x^5y^(n-5) is 11,628. Find the coefficient of x^5y^(n-4) in the expansion of (x+y)^(n+1). What is the value of n?

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- January 5th 2012, 12:00 PMkangta27Binomial Theorem
In the expansion of (x+y)^n the coefficient of x^4y^(n-4) is 3,876 and the coefficient of x^5y^(n-5) is 11,628. Find the coefficient of x^5y^(n-4) in the expansion of (x+y)^(n+1). What is the value of n?

- January 5th 2012, 04:20 PMRidleyRe: Binomial Theorem
Each coefficient can be calculated as follows:

(1)

(2)

Combine (1) and (2):

- January 5th 2012, 04:39 PMkangta27Re: Binomial Theorem
Thank you so much Ridley! My only question is, what happened to the (n-4)! and (n-5)! when you combined (1) and (2)?

- January 5th 2012, 04:44 PMRidleyRe: Binomial Theorem