Homework Help: Representation of function as power series

1. Nov 27, 2012

aero_zeppelin

1. The problem statement, all variables and given/known data
Represent 5x / (10 + x) as a power series, find c0, c1, c2, c3 and c4, find the radius of convergence

3. The attempt at a solution

I think I got the representation fine:

Ʃ from 0 to ∞ = 1/2 [ (-1^n)(x^n+1) / 10^n ]

But what the hell are those c0, c1 etc...? I thought they were the coefficients of the series but I keep getting them wrong...

My answers are: c0 = 1/2 , c1 = -1/20, c2 = 1/200 .....

2. Nov 27, 2012

Staff: Mentor

They are the coefficients of the series, with c0 being the constant term, c1 the coefficient of x, c2 the coefficient of x2, and so forth.

It looks like your coefficients are out of sync. You have what appear to be the right numbers, but the subscripts are off by one.

3. Nov 27, 2012

aero_zeppelin

It's been driving me crazy haha. Ok, so it should be:

c0 = ?
c1 = 1/2
c2 = -1/20
c3 = 1/200
c4 = -1/2000

So you just plug in "n" and see the respective coefficients? What happens with c0?

Thanks a lot

4. Nov 27, 2012

Staff: Mentor

c0 = 0

I didn't verify that your formula is correct, as I did this by dividing 5x by 10 + x using polynomial long division. The first few terms I got were (1/2)x - (1/20)x2 + (1/200)x3, and these coefficients agree with the ones you show.

Since there is no constant term, that means its coefficient is zero.

5. Nov 27, 2012

aero_zeppelin

Got it... Thanks so much!