Find I.C of :

(i)

(ii)

(iii)Ʃ n!

(iv)

Main methods of expanding a func. F(x) in power series (p.s) :

1-Using Taylor's and Maclourin's :

T.S for a func. F(x) around x=a is given by:

Maclourine's is T.S at a=0

find T.S and M.S for:

1- f(x)=

2-f(x)=cos(x)

expansion of ,sin(x),cos(x),sh(x),cosh(x),tan(x) in the book p.169

2-Differentiate binomial integration:

F(x) =

3-Partial fractions:

Expand F(x) = in P.S

Using p.f

F(x) =

3=a (1+2x) +b (1-x)

at x=1 a=1

at x=-0.5 b=2

F(x) =

=

I.C =-0.5<x<0.5

Ex: use p.s to find :

By substituting every x by