convergence: f(x) = sum[n=-infty, +infty] ( (-1)^n ) / ( a + (nb + c(x))^2 )

[new_flow]

Dear community,

I really hope someone is able to help me solving this exercise:

\(\displaystyle \displaystyle \Large{ f(x) = \sum_{n=-\infty}^{\infty}\, \dfrac{(-1)^n}{(a\, +\, (n*b\,+\,c(x))^2)} }\)

I need to simplify the last expression thus deleting summing up the series in a symbolic form. From what I understand, the term (-1)^n makes it so difficult, but I do think that there is someone much better then me.

 

[Deleted member 4993]

Dear community,

I really hope someone is able to help me solving this exercise:

\(\displaystyle f(x) = \sum_{n=-\infty}^{\infty} \frac{(-1)^n}{(a + (n*b+c(x))^2)}\)

I need to simplify the last expression thus deleting summing up the series in a symbolic form. From what I understand, the term (-1)^n makes it so difficult, but I do think that there is someone much better then me..

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

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[stapel]

...help me solving this exercise:

\(\displaystyle \displaystyle \Large{ f(x) = \sum_{n=-\infty}^{\infty}\, \dfrac{(-1)^n}{(a\, +\, (n*b\,+\,c(x))^2)} }\)

Are you given any information regarding "x", "a", "b", or "c(x)"? What were the instructions for this equation? What are you supposed to be doing with this?

I need to simplify the last expression....

Which part of the equation do you mean by "the last expression"?

...thus deleting summing up the series in a symbolic form.

I'm sorry, but I have no idea what this means. Kindly please clarify. For instance, do you maybe mean something like "collapsing the series into a closed-form expression, using no summation signs"...?

When you reply, please include a clear listing of your thoughts and efforts so far. Thank you!