1. ## power series representation.

a. need to differentiate 1/(1+x)^2 to find power series representation and the radius of convergence. (think that is the quotient rule)

(....= -2x/(1+x)^4 ??)

b. use part a to find power series 1/(1+x)^3

c. then use b to find power series for x^2/(1+x)^3

2. Originally Posted by rcmango
a. need to differentiate 1/(1+x)^2 to find power series representation and the radius of convergence. (think that is the quotient rule)

(....= -2x/(1+x)^4 ??)
um, the quotient rule is overkill. note that you have $\displaystyle (1 + x)^{-2}$ so the derivative is $\displaystyle -2(1 + x)^{-3} = \frac {-2}{(1 + x)^3}$

...i think you ate part of the question. the question probably said something to do with the second part of my hint for part (b)

b. use part a to find power series 1/(1+x)^3
Hint: find the power series of $\displaystyle \frac 1{(1 + x)^2}$ first. then differentiate the formula. you should be able to take it from there.

you can find the power series for $\displaystyle \frac 1{(1 + x)^2}$ by differentiating the formula for the power series of $\displaystyle \frac {-1}{1 + x}$...which you can find quite easily by considering the power series for $\displaystyle \frac 1{1 - x}$ ...something you should know by heart

c. then use b to find power series for x^2/(1+x)^3
multiply your answer in part (b) by $\displaystyle x^2$