What is the general binomial expansion?

• The?general?binomial?expansion, as given in the formula booklet, is

• If?n?∈???then the expansion is?finite?(see Binomial Expansion)
• Otherwise the expansion is infinitely long
  • It is only valid for?|x| < 1?(-1 < x < 1)
  • Only the first few terms of an expansion are usually needed

   

How do I use a binomial expansion to approximate a value?

• ?Ignoring higher powers of?x?leads to an approximation
• The more terms the closer the approximation is to the true value
• For most purposes, squared or cubed terms are accurate enough

STEP 1? Compare the value you are approximating to (a + bx)n
STEP 2? Solve the appropriate equation to find the value of?x
STEP 3? Substitute this value of?x?into the expansion to find the approximation