Writing power series as function












0












$begingroup$


I need to write the following power series as a function:



$2sum_{n=0}^infty (-1)^n x^{2n+1}$



I am not sure how to go about doing this.






calculus sequences-and-series power-series







share|cite|improve this question











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  • $begingroup$
    Hint: use a geometric series.
    $endgroup$
    – Sean Roberson
    Dec 8 '18 at 0:11










  • $begingroup$
    What do you mean "write it as a function"? It's already a function with domain $|x|<1. $ I guess what you mean is "find a simple formula for this function."
    $endgroup$
    – zhw.
    Dec 8 '18 at 1:45


















0












$begingroup$


I need to write the following power series as a function:



$2sum_{n=0}^infty (-1)^n x^{2n+1}$



I am not sure how to go about doing this.






calculus sequences-and-series power-series







share|cite|improve this question











$endgroup$












  • $begingroup$
    Hint: use a geometric series.
    $endgroup$
    – Sean Roberson
    Dec 8 '18 at 0:11










  • $begingroup$
    What do you mean "write it as a function"? It's already a function with domain $|x|<1. $ I guess what you mean is "find a simple formula for this function."
    $endgroup$
    – zhw.
    Dec 8 '18 at 1:45
















0












0








0





$begingroup$


I need to write the following power series as a function:



$2sum_{n=0}^infty (-1)^n x^{2n+1}$



I am not sure how to go about doing this.






calculus sequences-and-series power-series







share|cite|improve this question











$endgroup$




I need to write the following power series as a function:



$2sum_{n=0}^infty (-1)^n x^{2n+1}$



I am not sure how to go about doing this.






calculus sequences-and-series power-series




calculus sequences-and-series power-series






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 8 '18 at 0:24









Foobaz John

21.7k41352




21.7k41352










asked Dec 8 '18 at 0:07









ElijahElijah

626




626












  • $begingroup$
    Hint: use a geometric series.
    $endgroup$
    – Sean Roberson
    Dec 8 '18 at 0:11










  • $begingroup$
    What do you mean "write it as a function"? It's already a function with domain $|x|<1. $ I guess what you mean is "find a simple formula for this function."
    $endgroup$
    – zhw.
    Dec 8 '18 at 1:45




















  • $begingroup$
    Hint: use a geometric series.
    $endgroup$
    – Sean Roberson
    Dec 8 '18 at 0:11










  • $begingroup$
    What do you mean "write it as a function"? It's already a function with domain $|x|<1. $ I guess what you mean is "find a simple formula for this function."
    $endgroup$
    – zhw.
    Dec 8 '18 at 1:45


















$begingroup$
Hint: use a geometric series.
$endgroup$
– Sean Roberson
Dec 8 '18 at 0:11




$begingroup$
Hint: use a geometric series.
$endgroup$
– Sean Roberson
Dec 8 '18 at 0:11












$begingroup$
What do you mean "write it as a function"? It's already a function with domain $|x|<1. $ I guess what you mean is "find a simple formula for this function."
$endgroup$
– zhw.
Dec 8 '18 at 1:45






$begingroup$
What do you mean "write it as a function"? It's already a function with domain $|x|<1. $ I guess what you mean is "find a simple formula for this function."
$endgroup$
– zhw.
Dec 8 '18 at 1:45












1 Answer
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$begingroup$

Hints



The sum can be written as
$$
2xsum_{n=0}^infty (-x^2)^{n}
$$
and recall the formula for a geometric series.






share|cite|improve this answer









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    1 Answer
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    1 Answer
    1






    active

    oldest

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    active

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    votes






    active

    oldest

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    1












    $begingroup$

    Hints



    The sum can be written as
    $$
    2xsum_{n=0}^infty (-x^2)^{n}
    $$
    and recall the formula for a geometric series.






    share|cite|improve this answer









    $endgroup$


















      1












      $begingroup$

      Hints



      The sum can be written as
      $$
      2xsum_{n=0}^infty (-x^2)^{n}
      $$
      and recall the formula for a geometric series.






      share|cite|improve this answer









      $endgroup$
















        1












        1








        1





        $begingroup$

        Hints



        The sum can be written as
        $$
        2xsum_{n=0}^infty (-x^2)^{n}
        $$
        and recall the formula for a geometric series.






        share|cite|improve this answer









        $endgroup$



        Hints



        The sum can be written as
        $$
        2xsum_{n=0}^infty (-x^2)^{n}
        $$
        and recall the formula for a geometric series.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Dec 8 '18 at 0:23









        Foobaz JohnFoobaz John

        21.7k41352




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