I'm interested to know all the finite series that can be solved in a closed form (e.g. the geometric series)
2026-03-28 10:24:22.1774693462
Can you list all the finite series that can be solved in a closed form?
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Well, consider an arbitrary sequence $x_n$, then the sequence $x_{n+1}-x_{n}$ sums up to $x_n$, i.e. $$\sum_{i=1}^n(x_{i+1}-x_i)=x_{n+1}.$$ Therefore, any series (finite or infinite) is corresponded to a sequence.
In fact solving the sum of series (finite or infinite) is to find the corresponded sequence.