If a have a sequence such as the following:
$$a_0,a_1,a_2,\cdots$$
How can I find the summation representation for it, assuming it converges? I have searched a bit on MathExchange and found this Get sequence given the first few elements of the sequence. However, the sequences presented in OEIS are just integer ones. What about rationals? How should I proceed?
Thanks
EDIT
For example, let's say we have the following sequence: $$1, -\frac{1}{3}, \frac{1}{5}, -\frac{1}{7}, \cdots$$ As we can see, the summation can be rewritten as
$$\displaystyle\sum_{n=0}^\infty \left\lbrace \frac{(-1)^n}{2n+1} \right\rbrace$$
Which is the summation representation for the sequence above. The question is about how I can find a sigma sum for an arbitrary sequence. It is not necessary knowing its value, its sum.