My math books are very unclear and contradict each other regarding the defintion of a sequence and the definition of a series. I also checked wikipedia but it still isn't clear to me, so I tought I'd ask for some clarification here.

Here's what I know so far:

One of my books defines a sequence as "A function whose domain is the set of positive integers." That makes some intuitive sense, but in that case sequences can't be finite or start at a0, and that doesn't sound right. From wikipedia: "asequenceis an ordered list of objects (or events)."

Series is even more confusing. I have one book defining a series as "The sequence of partial sums {Sn} of a sequence {an}." Another one defines a series as "The sum of all the (infinite) elements of the sequence {an}." Wikipedia also mentions finite series, while my books only mentions infinite series.

Would appreciate any help with sorting this out! =)