Question

Find a power series representation of the function
\(f(x) =\large \frac{x}{2x^2+1}\)

Answer 1

@satellite73 @ganeshie8 @mathstudent55

Answer 2

they are doing these things where they are putting these in the form \(\frac{a}{1-r}\)m and then putting them into geometric sums. But I cant figure out how to do it with this one.

Answer 3

For |x| < 1,
\[\large \frac{1}{1-x} = \sum_{n=0}^{\infty} x^n,~~~~~~|x| \lt 1 \\
\large \frac{x}{2x^2+1} = \frac{x}{1-(-2x^2)} = x * \sum_{n=0}^{\infty} (-2x^2)^n =
\sum_{n=0}^{\infty} (-2)^nx^{2n+1}
\]

Answer 4

The second line above is the standard sum of an infinite geometric series:
1 + x + x^2 + x^3 + .... = 1 / (1-x)
for -1 < x < 1

For the given problem, the interval of convergence is:

\( \large
|-2x^2| < 1 \\ \large
-\frac{\sqrt{2}}{2} \lt x \lt \frac{\sqrt{2}}{2}
\)

Answer 5

asdf_movie

Answer 6

hi girl

Answer 7

hi samsonite

Answer 8

what u doin

Answer 9

i knew that

Answer 10

what ur number

Answer 11

naw jk can u help me

Answer 12

math
pre al

Answer 13

Which graph shows the solution for the inequality