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pbrown7916

  • 2 years ago

Sum of 2 power series: Given: f(x)=\sum_{n=3}^{\infty}\frac{ 2^{n} }{ n! }\left( x-1 \right)^{n-2} and g(x)=\sum_{n=1}^{\infty}\frac{ n ^{2} }{ 2^{n} }\left( x-1 \right)^{n-1} Find: f(x)+g(x)=\sum_{n=0}^{\infty}a _{n}\left( x-1 \right)^{n}

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  1. Skaematik
    • 2 years ago
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    What is (a-sub-n)x^n ?

  2. pbrown7916
    • 2 years ago
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    any constant

  3. pbrown7916
    • 2 years ago
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    haven't mastered entering equations here yet haha

  4. pbrown7916
    • 2 years ago
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    \[a_{n}\]

  5. pbrown7916
    • 2 years ago
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    so \[f(x)=\sum_{n=3}^{\infty}\frac{ 2^{n} }{ n! }\left( x-1 \right)^{n-2}\] and \[g(x)=\sum_{n=1}^{\infty}\frac{ n ^{2} }{ 2^{n} }\left( x-1 \right)^{n-1}\]

  6. pbrown7916
    • 2 years ago
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    and I need to find\[f(x)+g(x)=\sum_{n=0}^{\infty}a _{n}\left( x-1 \right)^{n}\]

  7. Skaematik
    • 2 years ago
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    Sorry not sure try physicsforums.com

  8. pbrown7916
    • 2 years ago
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    ok thanks skaematik

  9. pbrown7916
    • 2 years ago
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    This UI is rather annoying, sorry for the way my question is stated above.

  10. cinar
    • 2 years ago
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    \[\sum_{n=1}^{\infty}\frac{ 2^{n+1} }{ (n+1)! }\left( x-1 \right)^{n}+\sum_{n=0}^{\infty}\frac{(n+1)^{2} }{ 2^{n+1} }\left( x-1 \right)^{n}\]

  11. pbrown7916
    • 2 years ago
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    cinar, I thought something similar, but I have to force the solution to have the lower limit n=0

  12. cinar
    • 2 years ago
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    \[-1+\sum_{n=0}^{\infty}\frac{ 2^{n+1} }{ (n+1)! }\frac{(n+1)^{2} }{ 2^{n+1} }(x-1)^n\]

  13. cinar
    • 2 years ago
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    \[-1+\sum_{n=0}^{\infty}a_n(x-1)^n\]

  14. cinar
    • 2 years ago
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    this should be 2 sorry \[-2+\sum_{n=0}^{\infty}\frac{ 2^{n+1} }{ (n+1)! }\frac{(n+1)^{2} }{ 2^{n+1} }(x-1)^n\]

  15. cinar
    • 2 years ago
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    but it is not what you looking for right..

  16. pbrown7916
    • 2 years ago
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    thanks for your replies cinar, i appreciate the help. i suppose my real problem at this point is understanding how the solution from the book was reached...i'm trying to upload it now

  17. cinar
    • 2 years ago
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    \[-2+\sum_{n=0}^{\infty}\frac{ 2^{n+1} }{ (n+1)! }+\frac{(n+1)^{2} }{ 2^{n+1} }(x-1)^n\]

  18. pbrown7916
    • 2 years ago
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    here's what they got:

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  19. cinar
    • 2 years ago
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    glad to hear that..

  20. cinar
    • 2 years ago
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    yeah I see now where I made a mistake..

  21. pbrown7916
    • 2 years ago
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    oh? btw i'm looking at your problem...no ideas for it yet tho

  22. cinar
    • 2 years ago
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    thanks (:

  23. cinar
    • 2 years ago
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    I though it should be related integration by part somehow but no clue yet..

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