For some real number a and some positive integer n
The first few terms in the expansion of (1 + ax)n are 1- 20x + 150x2 + cx3 + ...
Thank you in advance
So for a=-5 and n=5 we have -20x = 4*(-5x), 150x2=6*(-5x)2, so the next term to follow is 4*(-5x)3 = -500x3. Thus c=-500.
(4, 6 and 4 are the three non-1 binomial coefficients for n=5, they can be found for example as numbers in the pascal's-triangle. I got a=5 and n=5 by looking at dividers of 20 - my first guess was 20=4*5, 4 as binomial-coefficient, so a had to be 5 - luckily it worked ;) )