Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
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.
 one year ago
 one year ago
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.
 one year ago
 one year ago

This Question is Closed

ns36Best ResponseYou've already chosen the best response.1
I'll try to make to write f(x) in the equation editor....one sec.
 one year ago

ns36Best ResponseYou've already chosen the best response.1
\[\sum_{0}^{\infty} ((1)^{n} x^{2n})/((2n)!)\]
 one year ago

ns36Best 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.
 one year ago

amistre64Best 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
 one year ago

amistre64Best ResponseYou've already chosen the best response.1
the summation is jsut a polynomial
 one year ago

amistre64Best 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
 one year ago

ns36Best ResponseYou've already chosen the best response.1
Oh I see, f(x) is just cos(x)! Thanks a lot!
 one year ago

amistre64Best ResponseYou've already chosen the best response.1
\[\sum_{0}^{\infty} \frac{(1)^{n} x^{2n}}{(2n)!}\] \[D_x[\sum ]=\sum_{1}^{\infty} \frac{(1)^{n} 2n\ x^{(2n1)}}{(2n)!}\] \[D_{xx}[\sum ]=\sum_{2}^{\infty} \frac{(1)^{n} 2n(2n1)\ x^{(2n2)}}{(2n)!}\]
 one year ago

amistre64Best 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
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.