Answer 2 Taylor Series Questions correctly to earn BEST ANSWER!?

Question

1) Consider the following function: f(x)= 1/x

A) Find the first four nonzero terms of the Taylor series fro the given function about -2. You will need to convert any factorials into integers.

B) Find an expression for the general term of the Taylor series assuming the starting value of the index, k is 0.


2) Consider the following function: f(x)= 1/(1-x)

A) Find the first four nonzero terms of the Taylor series fro the given function about 0. You will need to convert any factorials into integers.

B) Find an expression for the general term of the Taylor series assuming the starting value of the index, k is 0.

Answer 1

1/x= -1/2 -(x+2)*1/4 -(x+2)^2*1/8 -(x+2)^2*1/321/1-x

1/x= -1/2 -(x-2)/2^2 --- -(x-2)^n/2^(n+1)----

1/(1-x) =1+ x+x^2+x^3+x^4

1/(1-x= ) 1+x+x^2+++++ x^n++++++