Posted by **Anonymous** on Tuesday, November 16, 2010 at 11:21pm.

(a) Use differentiation to find power series representation for f(x)=1/(1+x)^2

What is the radius of convergence?

(b) Use part (a) to find a power series for f(x)=1/(1+x)^3

(c) Use part (b) to find a power series for f(x)=x^2/(1+x)^3

I found part (a) which was Σ n=0 to ∞ (1)^n(n+1)(x)^n, but I'm not sure how to use this for part (b). I thought something along the lines of:

1/(1+x)^3 = 1/(1+x)^2 * 1/(1+x)

and replace "1/(1+x)^2" with "Σ n=0 to ∞ (1)^n(n+1)(x)^n" Is this how I'm suppose to solve the problem?

## Answer this Question

## Related Questions

- Calculus - a) Find the Taylor series associated to f(x) = x^-2 at a = 1. Be sure...
- calc - f(x)=x^2/4+x^3 find the power series representation...so far i found ...Ó...
- Calculus - What is the radius of convergence of the power series (((2n)!x^(n...
- calculus - use the power series to estimate the series: from 0 to 4 of ln(1+x)dx...
- calculus - use the power series to estimate the series: from 0 to 4 of ln(1+x)dx...
- math quick question - Hi! Thank you for your help~~ What is the absolute value ...
- Taylor seires - f(x) =ln (1-x) a) Compute f'(x), f''(x), f'''(x). Spot the ...
- calculus - in the following series x is a real number. In each case use the ...
- calculus - state the power series of an appropriate familiar function and use it...
- College Calculus (Binomial Series) - Expand f(x) = (x+x^2)/((1-x)^3) as a power ...