Core Pure - Series (2) Flashcards
What is the theory of methods of difference
When you add terms in a series some terms will cancel so you know what the nth term is
What may make a method of difference question tricky?
Each term may not directly cancel. A term may skip a row then cancel with the next row
What term can be used to switch the sign every time the integer value of n increases?
What may a hard differentiation question look like and give the answer?
What is the theory behind the MacLaurin Expansion?
What did MacLaurin say?
When is the MacLaurin series a better approximation?
The approximation gets better hen abs(x) is small
Why can’t you find a macLaurin series for Inx?
It has an asymptote at x=0
How do you derive small angle approximations?
MacLaurin Series
How do you find the MacLaurin series for a function?
You need to differentiate the function a few times
Next to the differentiation function write f(0)=
Once you have the desired accuracy of the question write out the MacLaurin series
To do this write the terms in ascending powers of x^n/n! But ignoring any terms which have 0 in it (where n starts at 0)
If asked to find an approximation for a MacLaurin series what do you do?
Convert it into radians then sub it into the expansion
What is the MacLaurin expansion for
What is this the equivalence of this?
Proving binomial expansion
How would you find an MacLaurin expansion for
You write out the series expansion for e^x
You write out the series expansion for cosx
You sub the expansion for cosx into the e^x one
Simplify the expression
