Sequences and Series

 

Sequence:  

When some numbers are written in some particular order, we can call it a sequence. For, example, take the numbers 

1, 3, 5, 7, 9, . . . . 

Here, we have a sequence of odd numbers. It is started with the number 1, which is an odd number, and then each successive number is obtained by adding 2 to give the next odd number. 

Here is another sequence: 

1, 4, 9, 16, 25, . . . .  

Above is the sequence of square numbers.   

20, 25, 30, 35, ...  

Here, each successive number is obtained by adding 5 to give the next number and sequence started with 20. 

Series:  

When we add up all the terms of a sequence, we will get series. For example, below is a sequence

1, 2, 3, 4   

The corresponding series is the sum 1 + 2 + 3 + 4, and the value of the series is 10.
Series is denoted by capital letter 'S'.  S 4 =1+4+9+16=30.
Or it can be showed by the Greek letter, called 'sigma':   

For example, 

Here n is lower index and telling us that from where the counting will be started and k is upper index which telling that where the sequence will be stopped.