Pure Year 2 Unit 4

Question 1

Expand (1+x)^n

Answer 1

1 + nx + ((n(n-1))/2!)x^2 + ((n(n-1)(n-2))/3!)x^3 + …

Question 2

Expand (a+bx)^n

Answer 2

(a^n)(1+(b/a)x)^n

Question 3

When is the expansion of (1+x)^n valid?

Answer 3

When modulus(bx)<1 or modulus(x) < 1/modulus(b)

Question 4

When is the expansion of (a+bx)^n valid?

Answer 4

When modulus((b/a)/x) < 1 or modulus(x) < modulus(a/b)