Binomial Expansion

Question 1

What is Pascal’s triangle? (up to n=6)

Answer 1

……………1
…………1…..1
……….1….2…1
…….1….3…3….1
….1….4…6….4….1
..1…5…10..10…5…1
1..6..15..20..15..6…1

Question 2

What is the factorial?

Answer 2

a!
e.g. 3! = 3 x 2 x 1

Question 3

What do you do if the n is too high? (Binomial Expansion)

Answer 3

aCb
a = number of outcomes
b = number to choose

Question 4

How do you answer a question like:
Find the first 4 terms of f(x)^n. Then by using a suitable substitution, find an approximation for z?

Answer 4

Find the first four terms using aCb
Find a value for x that gives you z
Then sub the value into the terms

Question 5

How do you find the coefficient of x^z of (a + bx)^n

Answer 5

nCz x a^n-z x (bx)^z

Question 6

What is the binomial expansion equation?

Answer 6

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

Question 7

How do you find the range of validity?

Answer 7

solve for x inside the brackets
eg (x+1) –> |x|<1
no negatives for modulus

Question 8

How do you use binomial expansion on partial fractions?

Answer 8

solve partial fractions
convert the fractions into (x+1)^-a
solve