How to calculate this $sumlimits_{n=0}^{infty}frac{n}{2^n}e^{jwn}$












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How to calculate this $sumlimits_{n=0}^{infty}frac{n}{2^n}e^{-jwn}$,because it is not geometric progression,so i can't know how to solve it,can anyone help me?






sequences-and-series summation fourier-transform







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  • $begingroup$
    Still you can write your series as $$sum_{ngeq 0}frac{e^{-jwn}}{2^n}+sum_{ngeq 1}frac{e^{-jwn}}{2^n}+sum_{ngeq 2}frac{e^{-jwn}}{2^n}+ldots $$ which is a geometric series of geometric series.
    $endgroup$
    – Jack D'Aurizio
    Dec 4 '18 at 10:43










  • $begingroup$
    See math.stackexchange.com/questions/647587/…
    $endgroup$
    – lab bhattacharjee
    Dec 4 '18 at 10:43
















0












$begingroup$


How to calculate this $sumlimits_{n=0}^{infty}frac{n}{2^n}e^{-jwn}$,because it is not geometric progression,so i can't know how to solve it,can anyone help me?






sequences-and-series summation fourier-transform







share|cite|improve this question









$endgroup$












  • $begingroup$
    Still you can write your series as $$sum_{ngeq 0}frac{e^{-jwn}}{2^n}+sum_{ngeq 1}frac{e^{-jwn}}{2^n}+sum_{ngeq 2}frac{e^{-jwn}}{2^n}+ldots $$ which is a geometric series of geometric series.
    $endgroup$
    – Jack D'Aurizio
    Dec 4 '18 at 10:43










  • $begingroup$
    See math.stackexchange.com/questions/647587/…
    $endgroup$
    – lab bhattacharjee
    Dec 4 '18 at 10:43














0












0








0





$begingroup$


How to calculate this $sumlimits_{n=0}^{infty}frac{n}{2^n}e^{-jwn}$,because it is not geometric progression,so i can't know how to solve it,can anyone help me?






sequences-and-series summation fourier-transform







share|cite|improve this question









$endgroup$




How to calculate this $sumlimits_{n=0}^{infty}frac{n}{2^n}e^{-jwn}$,because it is not geometric progression,so i can't know how to solve it,can anyone help me?






sequences-and-series summation fourier-transform




sequences-and-series summation fourier-transform






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asked Dec 4 '18 at 10:38









electronic componentelectronic component

387




387












  • $begingroup$
    Still you can write your series as $$sum_{ngeq 0}frac{e^{-jwn}}{2^n}+sum_{ngeq 1}frac{e^{-jwn}}{2^n}+sum_{ngeq 2}frac{e^{-jwn}}{2^n}+ldots $$ which is a geometric series of geometric series.
    $endgroup$
    – Jack D'Aurizio
    Dec 4 '18 at 10:43










  • $begingroup$
    See math.stackexchange.com/questions/647587/…
    $endgroup$
    – lab bhattacharjee
    Dec 4 '18 at 10:43


















  • $begingroup$
    Still you can write your series as $$sum_{ngeq 0}frac{e^{-jwn}}{2^n}+sum_{ngeq 1}frac{e^{-jwn}}{2^n}+sum_{ngeq 2}frac{e^{-jwn}}{2^n}+ldots $$ which is a geometric series of geometric series.
    $endgroup$
    – Jack D'Aurizio
    Dec 4 '18 at 10:43










  • $begingroup$
    See math.stackexchange.com/questions/647587/…
    $endgroup$
    – lab bhattacharjee
    Dec 4 '18 at 10:43
















$begingroup$
Still you can write your series as $$sum_{ngeq 0}frac{e^{-jwn}}{2^n}+sum_{ngeq 1}frac{e^{-jwn}}{2^n}+sum_{ngeq 2}frac{e^{-jwn}}{2^n}+ldots $$ which is a geometric series of geometric series.
$endgroup$
– Jack D'Aurizio
Dec 4 '18 at 10:43




$begingroup$
Still you can write your series as $$sum_{ngeq 0}frac{e^{-jwn}}{2^n}+sum_{ngeq 1}frac{e^{-jwn}}{2^n}+sum_{ngeq 2}frac{e^{-jwn}}{2^n}+ldots $$ which is a geometric series of geometric series.
$endgroup$
– Jack D'Aurizio
Dec 4 '18 at 10:43












$begingroup$
See math.stackexchange.com/questions/647587/…
$endgroup$
– lab bhattacharjee
Dec 4 '18 at 10:43




$begingroup$
See math.stackexchange.com/questions/647587/…
$endgroup$
– lab bhattacharjee
Dec 4 '18 at 10:43










1 Answer
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For $|z|<1$ we have $sum_{n=0}^{infty}n z^n= frac{z}{(1-z)^2}$.



Now let $z= frac{e^{-jw}}{2}$. Can you proceed ?






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  • $begingroup$
    thx,i will see this math.stackexchange.com/questions/647587/…
    $endgroup$
    – electronic component
    Dec 4 '18 at 10:47











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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









2












$begingroup$

For $|z|<1$ we have $sum_{n=0}^{infty}n z^n= frac{z}{(1-z)^2}$.



Now let $z= frac{e^{-jw}}{2}$. Can you proceed ?






share|cite|improve this answer









$endgroup$













  • $begingroup$
    thx,i will see this math.stackexchange.com/questions/647587/…
    $endgroup$
    – electronic component
    Dec 4 '18 at 10:47
















2












$begingroup$

For $|z|<1$ we have $sum_{n=0}^{infty}n z^n= frac{z}{(1-z)^2}$.



Now let $z= frac{e^{-jw}}{2}$. Can you proceed ?






share|cite|improve this answer









$endgroup$













  • $begingroup$
    thx,i will see this math.stackexchange.com/questions/647587/…
    $endgroup$
    – electronic component
    Dec 4 '18 at 10:47














2












2








2





$begingroup$

For $|z|<1$ we have $sum_{n=0}^{infty}n z^n= frac{z}{(1-z)^2}$.



Now let $z= frac{e^{-jw}}{2}$. Can you proceed ?






share|cite|improve this answer









$endgroup$



For $|z|<1$ we have $sum_{n=0}^{infty}n z^n= frac{z}{(1-z)^2}$.



Now let $z= frac{e^{-jw}}{2}$. Can you proceed ?







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Dec 4 '18 at 10:44









FredFred

45.4k1848




45.4k1848












  • $begingroup$
    thx,i will see this math.stackexchange.com/questions/647587/…
    $endgroup$
    – electronic component
    Dec 4 '18 at 10:47


















  • $begingroup$
    thx,i will see this math.stackexchange.com/questions/647587/…
    $endgroup$
    – electronic component
    Dec 4 '18 at 10:47
















$begingroup$
thx,i will see this math.stackexchange.com/questions/647587/…
$endgroup$
– electronic component
Dec 4 '18 at 10:47




$begingroup$
thx,i will see this math.stackexchange.com/questions/647587/…
$endgroup$
– electronic component
Dec 4 '18 at 10:47


















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