Mixing
How to study the uniform convergence of $sumfrac{n^{n+1}x^{n}e^{-nx}}{n!} ? x geq 0$
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How to study the uniform convergence of $$sumfrac{n^{n+1}x^{n}e^{-nx}}{n!} $$
I was thinking about the Weierstrass M-test, but if we consider as $$f_n(x) =frac{n^{n+1}x^{n}e^{-nx}}{n!}$$.
The $f_n(x)$ takes max. value at $x=1$ so we consider $$M_n=frac{n^{n+1}e^{-n}}{n!}$$ but $M_n$ does not converge.
real-analysis analysis
asked Jan 27 at 20:06
ThecomonsThecomons
72
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add a comment |
$begingroup$
How to study the uniform convergence of $$sumfrac{n^{n+1}x^{n}e^{-nx}}{n!} $$
I was thinking about the Weierstrass M-test, but if we consider as $$f_n(x) =frac{n^{n+1}x^{n}e^{-nx}}{n!}$$.
The $f_n(x)$ takes max. value at $x=1$ so we consider $$M_n=frac{n^{n+1}e^{-n}}{n!}$$ but $M_n$ does not converge.
real-analysis analysis
asked Jan 27 at 20:06
ThecomonsThecomons
72
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I would use the change of variable $t:=xe^x$.
$endgroup$
– Yves Daoust
Jan 27 at 20:08
1
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Please, show that you have worked on your exercise...
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– Jean Marie
Jan 27 at 21:00
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I have edited and changed a typing mistake
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– Thecomons
Jan 27 at 21:12
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uniform convergence where?
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– zhw.
Jan 27 at 23:37
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for x >= 0. But probably i should closed the interval, for example $(0,a)$ idk
$endgroup$
– Thecomons
Jan 27 at 23:59
add a comment |
$begingroup$
How to study the uniform convergence of $$sumfrac{n^{n+1}x^{n}e^{-nx}}{n!} $$
I was thinking about the Weierstrass M-test, but if we consider as $$f_n(x) =frac{n^{n+1}x^{n}e^{-nx}}{n!}$$.
The $f_n(x)$ takes max. value at $x=1$ so we consider $$M_n=frac{n^{n+1}e^{-n}}{n!}$$ but $M_n$ does not converge.
real-analysis analysis
asked Jan 27 at 20:06
ThecomonsThecomons
72
$endgroup$
How to study the uniform convergence of $$sumfrac{n^{n+1}x^{n}e^{-nx}}{n!} $$
I was thinking about the Weierstrass M-test, but if we consider as $$f_n(x) =frac{n^{n+1}x^{n}e^{-nx}}{n!}$$.
The $f_n(x)$ takes max. value at $x=1$ so we consider $$M_n=frac{n^{n+1}e^{-n}}{n!}$$ but $M_n$ does not converge.
real-analysis analysis
real-analysis analysis
asked Jan 27 at 20:06
ThecomonsThecomons
72
asked Jan 27 at 20:06
ThecomonsThecomons
72
edited Jan 27 at 23:57
Thecomons
asked Jan 27 at 20:06
ThecomonsThecomons
72
asked Jan 27 at 20:06
ThecomonsThecomons
72
asked Jan 27 at 20:06
ThecomonsThecomons
72
72
$begingroup$
I would use the change of variable $t:=xe^x$.
$endgroup$
– Yves Daoust
Jan 27 at 20:08
1
$begingroup$
Please, show that you have worked on your exercise...
$endgroup$
– Jean Marie
Jan 27 at 21:00
$begingroup$
I have edited and changed a typing mistake
$endgroup$
– Thecomons
Jan 27 at 21:12
$begingroup$
uniform convergence where?
$endgroup$
– zhw.
Jan 27 at 23:37
$begingroup$
for x >= 0. But probably i should closed the interval, for example $(0,a)$ idk
$endgroup$
– Thecomons
Jan 27 at 23:59
add a comment |
$begingroup$
I would use the change of variable $t:=xe^x$.
$endgroup$
– Yves Daoust
Jan 27 at 20:08
1
$begingroup$
Please, show that you have worked on your exercise...
$endgroup$
– Jean Marie
Jan 27 at 21:00
$begingroup$
I have edited and changed a typing mistake
$endgroup$
– Thecomons
Jan 27 at 21:12
$begingroup$
uniform convergence where?
$endgroup$
– zhw.
Jan 27 at 23:37
$begingroup$
for x >= 0. But probably i should closed the interval, for example $(0,a)$ idk
$endgroup$
– Thecomons
Jan 27 at 23:59
$begingroup$
I would use the change of variable $t:=xe^x$.
$endgroup$
– Yves Daoust
Jan 27 at 20:08
$begingroup$
I would use the change of variable $t:=xe^x$.
$endgroup$
– Yves Daoust
Jan 27 at 20:08
1
1
$begingroup$
Please, show that you have worked on your exercise...
$endgroup$
– Jean Marie
Jan 27 at 21:00
$begingroup$
Please, show that you have worked on your exercise...
$endgroup$
– Jean Marie
Jan 27 at 21:00
$begingroup$
I have edited and changed a typing mistake
$endgroup$
– Thecomons
Jan 27 at 21:12
$begingroup$
I have edited and changed a typing mistake
$endgroup$
– Thecomons
Jan 27 at 21:12
$begingroup$
uniform convergence where?
$endgroup$
– zhw.
Jan 27 at 23:37
$begingroup$
uniform convergence where?
$endgroup$
– zhw.
Jan 27 at 23:37
$begingroup$
for x >= 0. But probably i should closed the interval, for example $(0,a)$ idk
$endgroup$
– Thecomons
Jan 27 at 23:59
$begingroup$
for x >= 0. But probably i should closed the interval, for example $(0,a)$ idk
$endgroup$
– Thecomons
Jan 27 at 23:59
add a comment |
1 Answer
1
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Hint: Study pointwise convergence first with the ratio test.
answered Jan 28 at 0:49
zhw.zhw.
74.7k43175
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add a comment |
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1 Answer
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1 Answer
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active
oldest
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$begingroup$
Hint: Study pointwise convergence first with the ratio test.
answered Jan 28 at 0:49
zhw.zhw.
74.7k43175
$endgroup$
add a comment |
$begingroup$
Hint: Study pointwise convergence first with the ratio test.
answered Jan 28 at 0:49
zhw.zhw.
74.7k43175
$endgroup$
add a comment |
$begingroup$
Hint: Study pointwise convergence first with the ratio test.
answered Jan 28 at 0:49
zhw.zhw.
74.7k43175
$endgroup$
Hint: Study pointwise convergence first with the ratio test.
answered Jan 28 at 0:49
zhw.zhw.
74.7k43175
answered Jan 28 at 0:49
zhw.zhw.
74.7k43175
answered Jan 28 at 0:49
zhw.zhw.
74.7k43175
answered Jan 28 at 0:49
zhw.zhw.
74.7k43175
74.7k43175
add a comment |
add a comment |
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$begingroup$
I would use the change of variable $t:=xe^x$.
$endgroup$
– Yves Daoust
Jan 27 at 20:08
1
$begingroup$
Please, show that you have worked on your exercise...
$endgroup$
– Jean Marie
Jan 27 at 21:00
$begingroup$
I have edited and changed a typing mistake
$endgroup$
– Thecomons
Jan 27 at 21:12
$begingroup$
uniform convergence where?
$endgroup$
– zhw.
Jan 27 at 23:37
$begingroup$
for x >= 0. But probably i should closed the interval, for example $(0,a)$ idk
$endgroup$
– Thecomons
Jan 27 at 23:59