Further Algebra (bionmial Expnasion , Partial Fraction)

Question 1

How to do binomial expansion for harder values of n

Answer 1

First follow general formula for expansion

1 + Nx + n(n-1)/2! X2 + n(n-1)(n-2) /3! X3

Now apply n inside

1) can only work for values -1<x<1 otherwise it would expand without limit
2) the more values the more accurate you get
3) if x is different coefficient it’s fine, but it MUST be 1 and so will have to factor out

Question 2

How to find the range of validity

Answer 2

Rmeemerb -1<x<1, so whatever x is put inside and manipulate

Question 3

I’d there are two rnages if validity, then how do you decide ?

Answer 3

Choose the one that satisfies BITH

Question 4

A tip, if there are repeating patterns and once suddenly wring what does this prolly mean

Answer 4

Yiu made a mistake, patterns like all positbe, all negative one moositve one negative etc

Question 5

So etiems put approximation back into the equation Orginal before expansion

Answer 5

This will helpnyou see a pattern

Question 6

What to remember about partial fractions when there is a REPEATED ROOT

Answer 6

Repeated root, means you need to include it twice, so the releated root once and the other too

Question 7

How can you use partial fractions to help binomial expand

Answer 7

Split fractions up and expand both of them

Question 8

What about partial fractions in integration

Answer 8

Same thing so,it them up to jsie

Question 9

Further maths partial fractions example?

Answer 9

Come back