# Thread: Representations of Functions as Power series

1. ## Representations of Functions as Power series

Find the first cofefficients

f(x)=7/(1+64x^2)= summation n=0 to infinity (c_n)(x^n)
c_1
c_2
c_3
c_4

I really don't know how to do this. I know you could right it as summation n=0 to infinity 7*(-1)^n (64x^2)^n i'm not even sure that it is even right. please help

2. Originally Posted by will_lansing
Find the first cofefficients

f(x)=7/(1+64x^2)= summation n=0 to infinity (c_n)(x^n)
c_1
c_2
c_3
c_4

I really don't know how to do this. I know you could right it as summation n=0 to infinity 7*(-1)^n (64x^2)^n i'm not even sure that it is even right. please help

Use either the binomial theorem, or McLaurin/Taylor series.

RonL

3. what is the binomial theorem, or McLaurin/Taylor series

4. Originally Posted by will_lansing
what is the binomial theorem, or McLaurin/Taylor series
What have you covered so far in your course? Also, what course is it?

see here for binomial theorem

and here for Taylor/Mclaurin series

RonL

5. I'm in Calc 2 and we just covered differentiation and integration of power series. so which of the two method is the best to use for this problem

6. Originally Posted by will_lansing
I'm in Calc 2 and we just covered differentiation and integration of power series. so which of the two method is the best to use for this problem
I would use the binomial expansion, because I can just write it down without
computing derivatives.

RonL