Given that $\displaystyle 1-x+x^2...+ (-x)^n$ is a powers series representation for $\displaystyle \frac{1}{x+1}$, find a power representaion for $\displaystyle \frac{x^3}{1+x^2}$
I can't find out how to do these.
all help appreciated.
Given that $\displaystyle 1-x+x^2...+ (-x)^n$ is a powers series representation for $\displaystyle \frac{1}{x+1}$, find a power representaion for $\displaystyle \frac{x^3}{1+x^2}$
I can't find out how to do these.
all help appreciated.
Knowing the sum of an infinite convergent geometric series to be $\displaystyle S_n = \frac{a}{1-r}$ where a is the first term and r is the common ratio, compare this to what they have given you.
For $\displaystyle \frac{x^3}{1+x^2}$ a is equal to x^3 and r is equal to -x^2. The first term will be x^3 and then multiply by -x^2 to generate the rest of the terms.
The power series representation of $\displaystyle \frac{x^3}{1+x^2}$ will be $\displaystyle x^3 - x^5 + x^7 - ... + (-1)^{n}x^{3+2n} $ provided that for the first term n=0
Nevermind, looks like chisigma beat me to it.