Pointwise and uniform convergence $sum_{n=1}^{infty}frac{(n+1)^n-n^n}{n!}x^{n^n}$
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I am in deadlock studyibg the pointwise and uniform convergence of the following series:
$$sum_{n=1}^{infty}frac{(n+1)^n-n^n}{n!}x^{n^n}$$
Maybe should I handle it as a power series? But how? Any tips?
power-series uniform-convergence pointwise-convergence
edited Jan 13 at 16:43
user
3,9851627
asked Jan 13 at 14:40
F.incF.inc
403110
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add a comment |
0
$begingroup$
I am in deadlock studyibg the pointwise and uniform convergence of the following series:
$$sum_{n=1}^{infty}frac{(n+1)^n-n^n}{n!}x^{n^n}$$
Maybe should I handle it as a power series? But how? Any tips?
power-series uniform-convergence pointwise-convergence
edited Jan 13 at 16:43
user
3,9851627
asked Jan 13 at 14:40
F.incF.inc
403110
$endgroup$
$begingroup$
Did you try d Alembert? I think it works well
$endgroup$
– Marine Galantin
Jan 13 at 14:44
1
$begingroup$
Hint: For $|x|lt1$, show that $|a_n|le(2n)^nx^{n^2}$. Then use the $n$th root test.
$endgroup$
– Barry Cipra
Jan 13 at 15:46
add a comment |
0
0
0
$begingroup$
I am in deadlock studyibg the pointwise and uniform convergence of the following series:
$$sum_{n=1}^{infty}frac{(n+1)^n-n^n}{n!}x^{n^n}$$
Maybe should I handle it as a power series? But how? Any tips?
power-series uniform-convergence pointwise-convergence
edited Jan 13 at 16:43
user
3,9851627
asked Jan 13 at 14:40
F.incF.inc
403110
$endgroup$
I am in deadlock studyibg the pointwise and uniform convergence of the following series:
$$sum_{n=1}^{infty}frac{(n+1)^n-n^n}{n!}x^{n^n}$$
Maybe should I handle it as a power series? But how? Any tips?
power-series uniform-convergence pointwise-convergence
power-series uniform-convergence pointwise-convergence
edited Jan 13 at 16:43
user
3,9851627
asked Jan 13 at 14:40
F.incF.inc
403110
edited Jan 13 at 16:43
user
3,9851627
asked Jan 13 at 14:40
F.incF.inc
403110
edited Jan 13 at 16:43
user
3,9851627
edited Jan 13 at 16:43
user
3,9851627
edited Jan 13 at 16:43
user
3,9851627
3,9851627
asked Jan 13 at 14:40
F.incF.inc
403110
asked Jan 13 at 14:40
F.incF.inc
403110
asked Jan 13 at 14:40
F.incF.inc
403110
403110
$begingroup$
Did you try d Alembert? I think it works well
$endgroup$
– Marine Galantin
Jan 13 at 14:44
1
$begingroup$
Hint: For $|x|lt1$, show that $|a_n|le(2n)^nx^{n^2}$. Then use the $n$th root test.
$endgroup$
– Barry Cipra
Jan 13 at 15:46
add a comment |
$begingroup$
Did you try d Alembert? I think it works well
$endgroup$
– Marine Galantin
Jan 13 at 14:44
1
$begingroup$
Hint: For $|x|lt1$, show that $|a_n|le(2n)^nx^{n^2}$. Then use the $n$th root test.
$endgroup$
– Barry Cipra
Jan 13 at 15:46
$begingroup$
Did you try d Alembert? I think it works well
$endgroup$
– Marine Galantin
Jan 13 at 14:44
$begingroup$
Did you try d Alembert? I think it works well
$endgroup$
– Marine Galantin
Jan 13 at 14:44
1
1
$begingroup$
Hint: For $|x|lt1$, show that $|a_n|le(2n)^nx^{n^2}$. Then use the $n$th root test.
$endgroup$
– Barry Cipra
Jan 13 at 15:46
$begingroup$
Hint: For $|x|lt1$, show that $|a_n|le(2n)^nx^{n^2}$. Then use the $n$th root test.
$endgroup$
– Barry Cipra
Jan 13 at 15:46
add a comment |
0
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$begingroup$
Did you try d Alembert? I think it works well
$endgroup$
– Marine Galantin
Jan 13 at 14:44
1
$begingroup$
Hint: For $|x|lt1$, show that $|a_n|le(2n)^nx^{n^2}$. Then use the $n$th root test.
$endgroup$
– Barry Cipra
Jan 13 at 15:46