Series {sequence, mathematics} {mathematical sequence} can have numbers or terms {ordered term} in sequence. Sequence has general term {general term, sequence} and follows rule. Example sequence is x, 2*x, 3*x, ... General term a(n) = n * x, where n is term position. The rule is that n increases by one.
separator
Commas separate sequence terms, as in 1, 2, 3, ...
types
Sequences can descend, ascend, or alternate. Sequence terms can approach number {convergent sequence}. Sequence terms can approach infinity {divergent sequence}. Sequence can be neither convergent nor divergent {indefinite sequence}. Sequence can increase, decrease, increase, and so on {oscillating sequence} {alternating sequence}.
Two sequences are equal {coincident sequence} if and only if all corresponding sequence terms are equal.
The only sequence whose first term equals zero, and whose n+1th term equals zero if nth term equals zero, is sequence of zeroes {induction axiom}. The only sequence whose first term equals one, and whose n+1th term equals k + 1 if nth term equals k, is the positive-integer sequence. The positive-integer series is the only sequence that has the number one and contains the positive integers.
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Date Modified: 2022.0225