anonymous
  • anonymous
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}
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
What is (a-sub-n)x^n ?
anonymous
  • anonymous
any constant
anonymous
  • anonymous
haven't mastered entering equations here yet haha

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anonymous
  • anonymous
\[a_{n}\]
anonymous
  • anonymous
so \[f(x)=\sum_{n=3}^{\infty}\frac{ 2^{n} }{ n! }\left( x-1 \right)^{n-2}\] and \[g(x)=\sum_{n=1}^{\infty}\frac{ n ^{2} }{ 2^{n} }\left( x-1 \right)^{n-1}\]
anonymous
  • anonymous
and I need to find\[f(x)+g(x)=\sum_{n=0}^{\infty}a _{n}\left( x-1 \right)^{n}\]
anonymous
  • anonymous
Sorry not sure try physicsforums.com
anonymous
  • anonymous
ok thanks skaematik
anonymous
  • anonymous
This UI is rather annoying, sorry for the way my question is stated above.
anonymous
  • anonymous
\[\sum_{n=1}^{\infty}\frac{ 2^{n+1} }{ (n+1)! }\left( x-1 \right)^{n}+\sum_{n=0}^{\infty}\frac{(n+1)^{2} }{ 2^{n+1} }\left( x-1 \right)^{n}\]
anonymous
  • anonymous
cinar, I thought something similar, but I have to force the solution to have the lower limit n=0
anonymous
  • anonymous
\[-1+\sum_{n=0}^{\infty}\frac{ 2^{n+1} }{ (n+1)! }\frac{(n+1)^{2} }{ 2^{n+1} }(x-1)^n\]
anonymous
  • anonymous
\[-1+\sum_{n=0}^{\infty}a_n(x-1)^n\]
anonymous
  • anonymous
this should be 2 sorry \[-2+\sum_{n=0}^{\infty}\frac{ 2^{n+1} }{ (n+1)! }\frac{(n+1)^{2} }{ 2^{n+1} }(x-1)^n\]
anonymous
  • anonymous
but it is not what you looking for right..
anonymous
  • anonymous
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
anonymous
  • anonymous
\[-2+\sum_{n=0}^{\infty}\frac{ 2^{n+1} }{ (n+1)! }+\frac{(n+1)^{2} }{ 2^{n+1} }(x-1)^n\]
anonymous
  • anonymous
here's what they got:
1 Attachment
anonymous
  • anonymous
glad to hear that..
anonymous
  • anonymous
yeah I see now where I made a mistake..
anonymous
  • anonymous
oh? btw i'm looking at your problem...no ideas for it yet tho
anonymous
  • anonymous
thanks (:
anonymous
  • anonymous
I though it should be related integration by part somehow but no clue yet..

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