Theory question 104
Binomial TheoremWrite down the first three terms of the binomial expansion (1 + ax)n in ascending powers of x. If the coefficients of x and x2 are 2 and 3/2 respectively, find the various values of a and n.
Show the model answer
Model answer
(1 + ax)n = 1 + nax + [n(n − 1)/2]a2x2 + ...
na = 2 and n(n − 1)a2/2 = 3/2, i.e. n(n − 1)a2 = 3
a = 2/n: n(n − 1)(4/n2) = 3, so 4(n − 1) = 3n
n = 4, a = ½
Explanation
Substitute a = 2/n into the second equation.