I cannot find a good explanation on how to represent a power series as a rational function. Thanks!

Santino Bautista

Santino Bautista

Answered question

2022-06-21

I cannot find a good explanation on how to represent a power series as a rational function. Thanks!
2 2 3 x + 2 9 x 2 2 27 x 3 + . . .

Answer & Explanation

Belen Bentley

Belen Bentley

Beginner2022-06-22Added 28 answers

To spell this out, your series can be written in the form of a geometric series:
2 ( 1 ( x 3 ) + ( x 3 ) 2 )
You can think of this as an infinite geometric series with r = x 3 and a=2 , so the fractional form is:
2 1 1 + x 3 = 6 x + 3
Reginald Delacruz

Reginald Delacruz

Beginner2022-06-23Added 7 answers

The Taylor series expansion of 6 x + 3 at x=0
6 x + 3 = 2 2 x 3 + 2 x 2 9 2 x 3 27 + 2 x 4 81 + O ( x 5 )

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