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high school Calculus B/C class homework:

1) Find a Series for f(x) = [tex]\frac{1}{1+x}[/tex] then find the interval of convergence.

i know that [tex]\frac{1}{1+x}[/tex] = 1-x+ [tex]x^{2}[/tex]-[tex]x^{3}[/tex]+...+ [tex]-x^{n}[/tex]+.... -1<x<1

but then i don`t understand how can i use the result from 1) to find 2) answer? since you guy will teach me how to do 2) then do i just do the same thing for 3) ?

2) Using your result from 1) find a series for [tex]\frac{1}{1+x^2}[/tex]

3) Using your result from 2) find a series for [tex]tan^{-1}x[/tex] then use your series to approximate [tex]\pi[/tex] to four decimal places. How many terms did you need?

1) Find a Series for f(x) = [tex]\frac{1}{1+x}[/tex] then find the interval of convergence.

i know that [tex]\frac{1}{1+x}[/tex] = 1-x+ [tex]x^{2}[/tex]-[tex]x^{3}[/tex]+...+ [tex]-x^{n}[/tex]+.... -1<x<1

but then i don`t understand how can i use the result from 1) to find 2) answer? since you guy will teach me how to do 2) then do i just do the same thing for 3) ?

2) Using your result from 1) find a series for [tex]\frac{1}{1+x^2}[/tex]

3) Using your result from 2) find a series for [tex]tan^{-1}x[/tex] then use your series to approximate [tex]\pi[/tex] to four decimal places. How many terms did you need?

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