C4- Binomial Expansion

Question 1

When is the binomial expansion of (1+x)^n finite and and exact?

Answer 1

When n is a positive integer

Question 2

When is the binomial expansion of (1+x)^2 infinite and approximate?

Answer 2

When n is any other rational number

e.g. negative or fractional powers

Question 3

When is the expansion of (1+ax)^2 valid, if the power is negative or fractional?

Answer 3

if |x|

Question 4

Why do you have to specify when the binomial expansion is valid if the power isn’t a positive integer?

Answer 4

To make sure it’s a converging series

Question 5

How do you change expressions in the form (a+bx)^n into the form of (1+cx)^n?

Answer 5

By taking out a factor of a

(a^n)(1+bx/a)^n

Question 6

What is the binomial expansion formula of (1+x)^n?

Answer 6

1+nx+((n(n-1))/2!)(x^2)+ etc