Limit of $ sum_{n=0}^{+infty} frac{(-x)^n}{1+n!} $ as $xrightarrow +infty$.












1












$begingroup$


The series of functions
$$
sum_{n=0}^{+infty} frac{(-x)^n}{1+n!}
$$
is pointwise convergent for any $xin mathbb{R}$, thus it defines the function $f:mathbb{R}rightarrow mathbb{R}$ given by $f(x) = sum_{n=0}^{+infty} frac{(-x)^n}{1+n!}$. Is there a way to evaluate the limit $lim_{xrightarrow +infty} f(x)$?






real-analysis calculus limits power-series







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$endgroup$












  • $begingroup$
    Do you mean, $f(x)=sum_{n=0}^{+infty} frac{(-x)^n}{1+n!}$?
    $endgroup$
    – Math Lover
    Jan 29 at 15:02


















1












$begingroup$


The series of functions
$$
sum_{n=0}^{+infty} frac{(-x)^n}{1+n!}
$$
is pointwise convergent for any $xin mathbb{R}$, thus it defines the function $f:mathbb{R}rightarrow mathbb{R}$ given by $f(x) = sum_{n=0}^{+infty} frac{(-x)^n}{1+n!}$. Is there a way to evaluate the limit $lim_{xrightarrow +infty} f(x)$?






real-analysis calculus limits power-series







share|cite|improve this question











$endgroup$












  • $begingroup$
    Do you mean, $f(x)=sum_{n=0}^{+infty} frac{(-x)^n}{1+n!}$?
    $endgroup$
    – Math Lover
    Jan 29 at 15:02
















1












1








1


3



$begingroup$


The series of functions
$$
sum_{n=0}^{+infty} frac{(-x)^n}{1+n!}
$$
is pointwise convergent for any $xin mathbb{R}$, thus it defines the function $f:mathbb{R}rightarrow mathbb{R}$ given by $f(x) = sum_{n=0}^{+infty} frac{(-x)^n}{1+n!}$. Is there a way to evaluate the limit $lim_{xrightarrow +infty} f(x)$?






real-analysis calculus limits power-series







share|cite|improve this question











$endgroup$




The series of functions
$$
sum_{n=0}^{+infty} frac{(-x)^n}{1+n!}
$$
is pointwise convergent for any $xin mathbb{R}$, thus it defines the function $f:mathbb{R}rightarrow mathbb{R}$ given by $f(x) = sum_{n=0}^{+infty} frac{(-x)^n}{1+n!}$. Is there a way to evaluate the limit $lim_{xrightarrow +infty} f(x)$?






real-analysis calculus limits power-series




real-analysis calculus limits power-series






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Feb 8 at 18:03







AlessioDV

















asked Jan 29 at 14:36









AlessioDVAlessioDV

1,158114




1,158114












  • $begingroup$
    Do you mean, $f(x)=sum_{n=0}^{+infty} frac{(-x)^n}{1+n!}$?
    $endgroup$
    – Math Lover
    Jan 29 at 15:02




















  • $begingroup$
    Do you mean, $f(x)=sum_{n=0}^{+infty} frac{(-x)^n}{1+n!}$?
    $endgroup$
    – Math Lover
    Jan 29 at 15:02


















$begingroup$
Do you mean, $f(x)=sum_{n=0}^{+infty} frac{(-x)^n}{1+n!}$?
$endgroup$
– Math Lover
Jan 29 at 15:02






$begingroup$
Do you mean, $f(x)=sum_{n=0}^{+infty} frac{(-x)^n}{1+n!}$?
$endgroup$
– Math Lover
Jan 29 at 15:02












1 Answer
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oldest

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$begingroup$

Write
$$
f(z) = sum_{n=0}^infty frac{z^n}{1+n!}
$$
of course an entire function. We want to know about $lim_{z to -infty} f(z)$. Maple produced this graph numerically.
f(z)



So I guess that $lim_{z to -infty} f(z) = +infty$.






share|cite|improve this answer









$endgroup$














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    1 Answer
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    1 Answer
    1






    active

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    0












    $begingroup$

    Write
    $$
    f(z) = sum_{n=0}^infty frac{z^n}{1+n!}
    $$
    of course an entire function. We want to know about $lim_{z to -infty} f(z)$. Maple produced this graph numerically.
    f(z)



    So I guess that $lim_{z to -infty} f(z) = +infty$.






    share|cite|improve this answer









    $endgroup$


















      0












      $begingroup$

      Write
      $$
      f(z) = sum_{n=0}^infty frac{z^n}{1+n!}
      $$
      of course an entire function. We want to know about $lim_{z to -infty} f(z)$. Maple produced this graph numerically.
      f(z)



      So I guess that $lim_{z to -infty} f(z) = +infty$.






      share|cite|improve this answer









      $endgroup$
















        0












        0








        0





        $begingroup$

        Write
        $$
        f(z) = sum_{n=0}^infty frac{z^n}{1+n!}
        $$
        of course an entire function. We want to know about $lim_{z to -infty} f(z)$. Maple produced this graph numerically.
        f(z)



        So I guess that $lim_{z to -infty} f(z) = +infty$.






        share|cite|improve this answer









        $endgroup$



        Write
        $$
        f(z) = sum_{n=0}^infty frac{z^n}{1+n!}
        $$
        of course an entire function. We want to know about $lim_{z to -infty} f(z)$. Maple produced this graph numerically.
        f(z)



        So I guess that $lim_{z to -infty} f(z) = +infty$.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Feb 8 at 22:34









        GEdgarGEdgar

        63.3k268172




        63.3k268172






























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