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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}
 one year ago
 one year 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}
 one year ago
 one year ago

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SkaematikBest ResponseYou've already chosen the best response.0
What is (asubn)x^n ?
 one year ago

pbrown7916Best ResponseYou've already chosen the best response.0
haven't mastered entering equations here yet haha
 one year ago

pbrown7916Best ResponseYou've already chosen the best response.0
so \[f(x)=\sum_{n=3}^{\infty}\frac{ 2^{n} }{ n! }\left( x1 \right)^{n2}\] and \[g(x)=\sum_{n=1}^{\infty}\frac{ n ^{2} }{ 2^{n} }\left( x1 \right)^{n1}\]
 one year ago

pbrown7916Best ResponseYou've already chosen the best response.0
and I need to find\[f(x)+g(x)=\sum_{n=0}^{\infty}a _{n}\left( x1 \right)^{n}\]
 one year ago

SkaematikBest ResponseYou've already chosen the best response.0
Sorry not sure try physicsforums.com
 one year ago

pbrown7916Best ResponseYou've already chosen the best response.0
ok thanks skaematik
 one year ago

pbrown7916Best ResponseYou've already chosen the best response.0
This UI is rather annoying, sorry for the way my question is stated above.
 one year ago

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

pbrown7916Best ResponseYou've already chosen the best response.0
cinar, I thought something similar, but I have to force the solution to have the lower limit n=0
 one year ago

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

cinarBest ResponseYou've already chosen the best response.0
\[1+\sum_{n=0}^{\infty}a_n(x1)^n\]
 one year ago

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

cinarBest ResponseYou've already chosen the best response.0
but it is not what you looking for right..
 one year ago

pbrown7916Best ResponseYou've already chosen the best response.0
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
 one year ago

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

pbrown7916Best ResponseYou've already chosen the best response.0
here's what they got:
 one year ago

cinarBest ResponseYou've already chosen the best response.0
yeah I see now where I made a mistake..
 one year ago

pbrown7916Best ResponseYou've already chosen the best response.0
oh? btw i'm looking at your problem...no ideas for it yet tho
 one year ago

cinarBest ResponseYou've already chosen the best response.0
I though it should be related integration by part somehow but no clue yet..
 one year ago
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