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ns36
Group Title
Help with sequences and series:
Show that the function f(x) = sum from 0 to infinity ((1)^n * x^(2n))/((2n)!) is a solution of the differential equation f''(x) + f(x) = 0.
 2 years ago
 2 years ago
ns36 Group Title
Help with sequences and series: Show that the function f(x) = sum from 0 to infinity ((1)^n * x^(2n))/((2n)!) is a solution of the differential equation f''(x) + f(x) = 0.
 2 years ago
 2 years ago

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ns36 Group TitleBest ResponseYou've already chosen the best response.1
I'll try to make to write f(x) in the equation editor....one sec.
 2 years ago

ns36 Group TitleBest ResponseYou've already chosen the best response.1
\[\sum_{0}^{\infty} ((1)^{n} x^{2n})/((2n)!)\]
 2 years ago

ns36 Group TitleBest ResponseYou've already chosen the best response.1
That's f(x), and I need to show that it's a solution to the differential equation f''(x) + f(x) = 0.
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.1
take the second derivative of the sumation and add it to the sumation itself to see if it goes to 0
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.1
the summation is jsut a polynomial
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.1
in teh eq editor, if you type in \frac{}{} you can fill in the {}s with your top and bottom arguments
 2 years ago

ns36 Group TitleBest ResponseYou've already chosen the best response.1
Oh I see, f(x) is just cos(x)! Thanks a lot!
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.1
\[\sum_{0}^{\infty} \frac{(1)^{n} x^{2n}}{(2n)!}\] \[D_x[\sum ]=\sum_{1}^{\infty} \frac{(1)^{n} 2n\ x^{(2n1)}}{(2n)!}\] \[D_{xx}[\sum ]=\sum_{2}^{\infty} \frac{(1)^{n} 2n(2n1)\ x^{(2n2)}}{(2n)!}\]
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.1
lol, that too
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.1
i think i need more practice on my summation derivatives :) but your way is sufficient i believe
 2 years ago
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