SOLUTION: The first three terms in the binomial expansion of (1+ kx)n are 1− 21x +189x2. Find the value of n and the value of k. Please show all the steps etc... I know the answe

Algebra ->  Sequences-and-series -> SOLUTION: The first three terms in the binomial expansion of (1+ kx)n are 1− 21x +189x2. Find the value of n and the value of k. Please show all the steps etc... I know the answe      Log On


   

Question 367543: The first three terms in the binomial expansion of (1+ kx)n are 1− 21x +189x2.
Find the value of n and the value of k.
Please show all the steps etc... I know the answer, but I don't understand the solution at all... thanks
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The first three terms of the expression %281%2Bkx%29%5En are 1%2B%28nk%29x%5E1+%2B+%28n%28n-1%29%2F2%29%2Ak%5E2x%5E2. Hence
nk = -21, and
%28n%28n-1%29%2F2%29k%5E2+=+189, after equating coefficients.
The foregoing equation is the same as %28n%5E2k%5E2-%28nk%29%2Ak%29%2F2+=+189. Hence
by substitution,
%28%28-21%29%5E2%2B21k%29%2F2+=+189, or 441%2B21k+=+378,
or 21k = -63, or k = -3. From nk = -21, n = 7.