+0  
 
0
51
2
avatar

For some real number a and some positive integer n

The first few terms in the expansion of (1 + ax)n are 1- 20x + 150x+ cx3 + ...    

 

Find c

 

Thank you in advance

 Mar 14, 2021
 #1
avatar+1776 
0

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 ;) )

 Mar 14, 2021
 #2
avatar
0

Thank you so much

Guest Mar 14, 2021

23 Online Users

avatar
avatar