# Help with power series representation

1. Dec 4, 2006

### bobbarkernar

1. The problem statement, all variables and given/known data

find a power series representation for the function and determine the radius of convergence.

f(t)= ln(2-t)

2. Relevant equations

3. The attempt at a solution

i first took the derivative of ln(2-t) which is 1/(t-2)

then i tried to write the integral 1/(t-2) in the form of a power series i got the sum for n=0 to infinity of (t/2)^n i don't know if this is write if someone can please help me

2. Dec 4, 2006

If $f(t) = \ln(2-t) [/tex] then write this as follows: [itex] -\ln(2-t) = \int \frac{1}{2-t} \; dt [/tex] How would you transform [itex] \frac{1}{2-t} [/tex] into a more recognizable form: i.e. [itex] \frac{1}{1-t}$?

3. Dec 4, 2006

### bobbarkernar

i would factor out a 1/2 so i would have (1/2)*1/(1-(1/2t))

4. Dec 4, 2006

ok then what would you do?

5. Dec 4, 2006

### bobbarkernar

i would write that as a power series:
(1/2)*the sum for n=0 to infinity of (1/2t)^n

6. Dec 4, 2006

correct you have:

$$\frac{1}{2}\sum_{n=0}^{\infty} (\frac{t}{2})^{n}$$

7. Dec 4, 2006

### bobbarkernar

8. Dec 4, 2006

or write it like this:

$$\sum_{n=0}^{\infty} \left(\frac{t^{n}}{2^{n+1}}\right)$$

9. Dec 4, 2006

### bobbarkernar

ok thank you very much

10. Mar 31, 2009

### joeG215

I'm confused... What happens to the integral?