|Class 11 Maths Sequences Series||Finite & infinite|
The various numbers occurring in a sequence are called its terms. We denote the terms of a sequence by a1, a2, a3, …, an, …, etc., the subscripts denote the position of the term. The nth term is the number at the nth position of the sequence and is denoted by an. The nth term is also called the general term of the sequence.
A sequence containing finite number of terms is called a finite sequence.
A sequence is called infinite, if it is not a finite sequence.
Let a1, a2, a3,…,an, be a given sequence. Then, the expression a1 + a2 + a3 +,…+ an +... is called the series associated with the given sequence .The series is finite or infinite according as the given sequence is finite or infinite.
Series are often represented in compact form, called sigma notation, using the Greek letter Σ (sigma) as means of indicating the summation involved. Thus, the series a1 + a2 + a3+ ... + an is abbreviated as