Factual Questions
1.What is a sequences?
A sequence is a list of numbers arranged according to a rule and is separated by commas is known as sequences.
For example; 1,2,3,4,5,
2. What is a series ?
The sum of terms of a sequence is series.
For example; 1+2+3+4……
There are different types of series ; Arithmetic series, geometric series, convergent series and divergent series.
Arithmetic Series : A types of series which involves addition or subtraction of a sequence in a sequence is known as arithmetic series.For example; 1+2+3+4…….1000000. The first term is a¡ and the constant difference is d and the number of terms is n.
Geometric series: A series which involves division or multiplication is known as geometric sequence.It has a constant ratio between terms. For example; 2+6+18+54. The first term is a¡ and the common ratio is r and the number of term is n.
Convergent Series: A series in which there is a limit to the partial sum. For example; 0.9,0.09.0.009,0.0009,…….1. The series converges to 1.
Divergent Series: A series which has no limit. It does not diverge . For example:1, 1+2, 1+2+3, 1+2+3+4,…..
3.How can we distinguish between and analyse different types of sequences and series?
Series is a sum of terms which can be arithmetic or geometric. Series are always infinite.If the series have a constant term its means that its is arithmetic. Where if it has constant ratio it means it is geometric sequence.