Question

Find the first five non-zero terms of power series representation centered at x=0 for the function below:

7/(1-x^2)

I get that the first term in the series is 7, but I have no clue how to find the other terms. Do I derive the equation? Help.

Answer 1

$$\frac1{1-x}=1+x+x^2+x^3+x^4+\dots\\\frac1{1-x^2}=1+x^2+x^4+x^6+x^8+\dots\\\frac7{1-x^2}=7+7x^2+7x^4+7x^6+7x^8\dots$$

Answer 2

Can I ask how you did it? do you just convert to power series and solve?

Answer 3

well, I used knowledge of geometric series to write it in this form. you can also do it using Taylor's theorem

Answer 4

you can also just do the division ...

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1 - x^2 | 7