Sequences:
Sequences also called Progressions,are used to represent ordered lists of numbers. Thus a sequence is a function whose domain is a subset of the set of natural numbers. Sequences are usually named with letters a, b, c etc., and n is used instead of x as a variable.
For example, the term of the sequence {n + (-1)n} can be written by assigning to n, the values 1, 2, 3,..... If we denote the sequence by {bn}, then bn = n + (-1)n.
Real Sequence:
If all members of a sequence are real numbers, then it is called a real sequence.
Series:
The sum of an indicated number of terms in a sequence is called a series. For example, the sum of the first seven terms of the sequence {n²} is the series,
Sequences also called Progressions,are used to represent ordered lists of numbers. Thus a sequence is a function whose domain is a subset of the set of natural numbers. Sequences are usually named with letters a, b, c etc., and n is used instead of x as a variable.
For example, the term of the sequence {n + (-1)n} can be written by assigning to n, the values 1, 2, 3,..... If we denote the sequence by {bn}, then bn = n + (-1)n.
Real Sequence:
If all members of a sequence are real numbers, then it is called a real sequence.
Series:
The sum of an indicated number of terms in a sequence is called a series. For example, the sum of the first seven terms of the sequence {n²} is the series,
1 + 4 + 9 + 16 + 25 + 36 + 49.
The above series is also named as the 7th partial sum of the sequence {n²}.
If the number of terms in a series is finite, then the series is called a finite series, while a series consisting of an unlimited number of terms is termed as an infinite series.
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