Maclaurin Series Question

[reis]

Find the power series of f(x)=(x² -5x-2)/(3x²-4x-4) at x=0, and find the interval of converge of the series

I thinked that The question could solved by maclaurin theorem but I couldn't do that I haven't seen a series question with a numerator and denominator. I used a calculator, it gave me first 5 element =>1/2 , 3x/4 , -5x²/8 , 19x³/6 , -53x⁴/32



I made an effort, couldn't solve it, Thanks for your help

 

[Deleted member 4993]

Find the power series of f(x)=(x² -5x-2)/(3x²- 4x - x) at x=0, and find the interval of converge of the series

I made an effort, couldn't solve it, Thanks for your help

Please show us what you have tried and exactly where you are stuck.

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https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

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[Romsek]

You can use partial fractions to break this up into a sum of simpler forms.

In particular you can reduce the terms to the form [MATH]\dfrac{1}{a x + b}[/MATH] which has a power series of

[MATH]\sum \limits_{k=0}^\infty~(-1)^{k} \dfrac{b^{k}}{a^{k+1}}x^k[/MATH] at [MATH]x=0[/MATH]

 

[Steven G]

Did you try to do the long division. Who knows maybe it will turn out nice. That is what I would first. If that was not helpful then I would try something else.