Power Series Expansion of f(x) = \frac{10}{1+100*x^2}

[ProBasket]

the function [tex]f(x) = \frac{10}{1+100*x^2}[/tex]
is represented as a power series
[tex] f(x) = \sum_{n=0}^{\infty} C_nX^n[/tex]

Find the first few coefficients in the power series:
C_0 = ____
C_1 = ____
C_2 = ____
C_3 = ____
C_4 = ____


well [tex]f(x) = \frac{10}{1+100*x^2}[/tex] can be written as [tex]10\sum_{n=0}^{\infty} (-100x^2)^n[/tex]

for C_0, i got 10 because if you plug in n = 0, you get 10 (which is correct).
for c_1, when i plug in n=1, i get -1000, which is incorrect.
i tried doing the same for c_2-c_4, but it keeps telling me i get the wrong answer. does anyone know why?

 

[whozum]

Im pretty sure you modeled the function incorrectly.

 

[Galileo]

Write out a few terms of your expansion. What are the coefficients of the even powers of x in your expansion?

 

[Data]

and more importantly, what are the coefficients of the odd powers of x?

 

[ProBasket]

i don't think i modeled it incorrectly, because there's a similar problem in the book, but maybe i made a mistake so who knows, but here are the first few terms...

10 - 1000x^2 + 10000x^4 -10000000x^6 + 1000000000x^8...

coefficients of the odd powers are zero...

but i can't seem to get the even coefficients correctly... what am i doing wrong?

 

[Data]

Looks fine to me except that your coefficient for [itex]x^4[/itex] is one power of ten too small. Remember that this expansion is only valid for [itex]|x|<1/10[/itex] too.