- #1

Richter915

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I'm supposed to find the following function as a Maclaurin Series. Please check if I'm correct.

f(x) = ln(1+x)

[tex]\sum \frac{\(x^n)((-1)^{n+1})}{n}[/tex]

and that sum goes from n=1 to [tex]\infty[/tex]

I also have to find the following functions as power series so please check it for me!

[tex]f(x) = \frac{1}{1+9x^2} = 9\sum \{(-1)^n}{x^{2n}\\

\\f(x) = \frac{1+x^2}{1-x^2} = \sum \{(x)^2}+{x^{2n+2}}[/tex]

those should be two separate functions but I don't know how to separate them into two lines. both of these series go from n=0 to [tex]\infty[/tex]

f(x) = ln(1+x)

[tex]\sum \frac{\(x^n)((-1)^{n+1})}{n}[/tex]

and that sum goes from n=1 to [tex]\infty[/tex]

I also have to find the following functions as power series so please check it for me!

[tex]f(x) = \frac{1}{1+9x^2} = 9\sum \{(-1)^n}{x^{2n}\\

\\f(x) = \frac{1+x^2}{1-x^2} = \sum \{(x)^2}+{x^{2n+2}}[/tex]

those should be two separate functions but I don't know how to separate them into two lines. both of these series go from n=0 to [tex]\infty[/tex]

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