If (1-(1/a))^6 is expanded, What is thesum of the last 3 coefficients?

Answer 1

The answer is 10. Here's why:

Your expression is equivalent to this: [1+ (-1/a)]^6, where a = 1 and b = -1/a. If we expand the expression (a + b)^6, we get this polynomial:

a^6 + 6 a^5 b + 15 a^4 b² + 20 a³ b³ + 15 a² b^4 + 6 a b^5 + b^6

Now, when we let a = 1 and b = - 1/a, we get this for the last three terms:

15 a² b^4 = 15 (1)² (-1/a)^4 = 15 (1/a)^4
6 a b^5 = 6 (1) (-1/a)^5 = 6 [(-1)^5 / a^5] = - 6 (1/a)^5
b^6 = (-1/a)^6 = 1/a^6 = 1 (1/a)^6

The sum of the last three coefficients is 15 - 6 + 1 = 10, which is your answer.