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 2 years ago
Sum of 2 power series:
Given: f(x)=\sum_{n=3}^{\infty}\frac{ 2^{n} }{ n! }\left( x1 \right)^{n2} and g(x)=\sum_{n=1}^{\infty}\frac{ n ^{2} }{ 2^{n} }\left( x1 \right)^{n1}
Find: f(x)+g(x)=\sum_{n=0}^{\infty}a _{n}\left( x1 \right)^{n}
 2 years ago
Sum of 2 power series: Given: f(x)=\sum_{n=3}^{\infty}\frac{ 2^{n} }{ n! }\left( x1 \right)^{n2} and g(x)=\sum_{n=1}^{\infty}\frac{ n ^{2} }{ 2^{n} }\left( x1 \right)^{n1} Find: f(x)+g(x)=\sum_{n=0}^{\infty}a _{n}\left( x1 \right)^{n}

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Skaematik
 2 years ago
Best ResponseYou've already chosen the best response.0What is (asubn)x^n ?

pbrown7916
 2 years ago
Best ResponseYou've already chosen the best response.0haven't mastered entering equations here yet haha

pbrown7916
 2 years ago
Best ResponseYou've already chosen the best response.0so \[f(x)=\sum_{n=3}^{\infty}\frac{ 2^{n} }{ n! }\left( x1 \right)^{n2}\] and \[g(x)=\sum_{n=1}^{\infty}\frac{ n ^{2} }{ 2^{n} }\left( x1 \right)^{n1}\]

pbrown7916
 2 years ago
Best ResponseYou've already chosen the best response.0and I need to find\[f(x)+g(x)=\sum_{n=0}^{\infty}a _{n}\left( x1 \right)^{n}\]

Skaematik
 2 years ago
Best ResponseYou've already chosen the best response.0Sorry not sure try physicsforums.com

pbrown7916
 2 years ago
Best ResponseYou've already chosen the best response.0This UI is rather annoying, sorry for the way my question is stated above.

cinar
 2 years ago
Best ResponseYou've already chosen the best response.0\[\sum_{n=1}^{\infty}\frac{ 2^{n+1} }{ (n+1)! }\left( x1 \right)^{n}+\sum_{n=0}^{\infty}\frac{(n+1)^{2} }{ 2^{n+1} }\left( x1 \right)^{n}\]

pbrown7916
 2 years ago
Best ResponseYou've already chosen the best response.0cinar, I thought something similar, but I have to force the solution to have the lower limit n=0

cinar
 2 years ago
Best ResponseYou've already chosen the best response.0\[1+\sum_{n=0}^{\infty}\frac{ 2^{n+1} }{ (n+1)! }\frac{(n+1)^{2} }{ 2^{n+1} }(x1)^n\]

cinar
 2 years ago
Best ResponseYou've already chosen the best response.0\[1+\sum_{n=0}^{\infty}a_n(x1)^n\]

cinar
 2 years ago
Best ResponseYou've already chosen the best response.0this should be 2 sorry \[2+\sum_{n=0}^{\infty}\frac{ 2^{n+1} }{ (n+1)! }\frac{(n+1)^{2} }{ 2^{n+1} }(x1)^n\]

cinar
 2 years ago
Best ResponseYou've already chosen the best response.0but it is not what you looking for right..

pbrown7916
 2 years ago
Best ResponseYou've already chosen the best response.0thanks 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

cinar
 2 years ago
Best ResponseYou've already chosen the best response.0\[2+\sum_{n=0}^{\infty}\frac{ 2^{n+1} }{ (n+1)! }+\frac{(n+1)^{2} }{ 2^{n+1} }(x1)^n\]

pbrown7916
 2 years ago
Best ResponseYou've already chosen the best response.0here's what they got:

cinar
 2 years ago
Best ResponseYou've already chosen the best response.0yeah I see now where I made a mistake..

pbrown7916
 2 years ago
Best ResponseYou've already chosen the best response.0oh? btw i'm looking at your problem...no ideas for it yet tho

cinar
 2 years ago
Best ResponseYou've already chosen the best response.0I though it should be related integration by part somehow but no clue yet..
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