For some real number a and some positive integer n, the first few terms in the expansion of (1 + ax)^n are
1 + 10x + 150 x^2 + cx^3 + ...
Find c.
\((1+ax)^n=1+nax+\frac{n(n-1)}{2!}a^2x^2+\frac{n(n-1)(n-2)}{3!}a^3x^3+...\)
Let \(na=10\)
and \(\frac{n(n-1)}{2!}a^2=150\)
and solve for a and n, then find c from \(c=\frac{n(n-1)(n-2)}{3!}a^3\)
