SOLUTION: The binomial (1+kx)^n where n>3. The coefficient of x^2 and x^3 are equal. Find k in terms of n

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Question 1071260: The binomial (1+kx)^n where n>3. The coefficient of x^2 and x^3 are equal. Find k in terms of n
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The terms in x3 and k2  in 
the expansion of (1+kx)n  are respectively

%28matrix%282%2C1%2Cn%2Cn-3%29%29k%5E3x%5E3 and %28matrix%282%2C1%2Cn%2Cn-2%29%29k%5E2x%5E2

The coefficients are

%28matrix%282%2C1%2Cn%2Cn-3%29%29k%5E3 and %28matrix%282%2C1%2Cn%2Cn-2%29%29k%5E2

Since they are equal,

%28matrix%282%2C1%2Cn%2Cn-3%29%29k%5E3%22%22=%22%22%28matrix%282%2C1%2Cn%2Cn-2%29%29k%5E2

%28matrix%282%2C1%2Cn%2Cn-3%29%29k%22%22=%22%22%28matrix%282%2C1%2Cn%2Cn-2%29%29

%28matrix%282%2C1%2Cn%2C3%29%29k%22%22=%22%22%28matrix%282%2C1%2Cn%2C2%29%29

%28%28n%28n-1%29%28n-2%29%29%2F3%21%29k%22%22=%22%22n%28n-1%29%2F2%21

%28%28n-2%29%29%2F3%21%29k%22%22=%22%221%2F2%21

%28%28n-2%29%29%2F6%29k%22%22=%22%221%2F2

%28n-2%29k%22%22=%22%223

k%22%22=%22%223%2F%28n-2%29

Edwin