(2) Series

Method of difference steps

1) put into a valid form e.g. f(r) - f(r+1) or similar (Most often given to you or is a partial fraction)

2) enter in the first few r values and learn a pattern

3) enter in the last few terms

4) cancel out the pattern leaving only a few values at the start and end

5) add them up and apply any factor taken out

Maclaurin series base formula

f(x)=f(0)+ f’(0)x + (f’’(0) /2!)x² + … + (f^r(r) (0) /r!) x^r + …

finding range of valid expansions

replace the x in the formula with your X divide back down to it being just X so you have a new valid range

Method of difference example image

Example 1 in book