Question

The function f(x)=1/(1+25x^2) is represented as a power series:
f(x)=∑n=0∞cnxn

Find the first few coefficients in the power series.
c0=
c1=
c2=
c3=
c4=

Find the radius of convergence R of the series.
R=

Answer 1

HI!!

Answer 2

for some reason I can't get c1-c5

Answer 3

I've gotten c0 and R

Answer 4

Hi :)

Answer 5

the most well known one is
\[\frac{1}{1-x}=\sum x^n\] right?

Answer 6

Yeah I've got that

Answer 7

I've even gotten a summation that I thought worked

Answer 8

replace \(x\) by \(-25x^2\)

Answer 9

but apparenlty it's wrong

Answer 10

yup I did that :)

Answer 11

did you get
\[1-25x^2+625x^4-...\]

Answer 12

I thought the summation is \[\sum_{0}^{\inf} (-25x^2)^n\]

Answer 13

that is the first three anyways
the number get big fast

Answer 14

Yes that's what I got

Answer 15

but the program I'm using for my uni says that's wrong

Answer 16

lets check

Answer 17

maybe the program is just wrong

Answer 18

http://www.wolframalpha.com/input/?i=1%2F%281%2B25x%5E2%29+

Answer 19

maybe they just want you to write it differently

Answer 20

\[\sum_{n=0}^{\infty} (-1)^{n}(25x)^{2n}\]

Answer 21

It just want's the coefficients, I even tried (-1)^1(5)^2

Answer 22

I think you meant \[\sum_{0}^{\inf}(-1)^n(5x)^{2n}\]

Answer 23

Thanks at least I feel I'm not going crazy now. I will check with my prof later