Infinite Sequences and Series
Definition
Infinite sequences are lists of numbers that continue indefinitely, while infinite series are sums of those numbers. They can converge to a finite value or diverge to infinity.
Analogy
Imagine trying to fill up a bucket with water drop by drop. If you keep adding drops forever, you have an infinite sequence. But if you add up all those drops, you get the total amount of water in the bucket, which is an infinite series.
Related terms
Convergence: When an infinite sequence or series approaches a finite value as more terms are added.
Divergence: When an infinite sequence or series does not approach a finite value and instead goes to infinity or negative infinity.
Geometric Series: A specific type of infinite series where each term is multiplied by a common ratio.
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