. Series The sum of the terms of a sequence is called series . Let a a a a n ,..., ,... be the sequence of real numbers.
Then the real number a + is defined as the series of real numbers. If a series has finite number of terms then it is called a Finite series . If a series has infinite number of terms then it is called an Infinite series . Let us focus our attention only on studying finite series.
Numbers and Sequences . . Sum to n terms of an A.P. A series whose terms are in Arithmetic progression is called Arithmetic series.
Let a a d a d a ,... be the Arithmetic Progression. The sum of first n terms of a Arithmetic Progression denoted by S n is given by, S n = ) ) ... ( ) Rewriting the above in reverse order S n = ) ) ) ) ...
( ) Adding ( ) and ( ) we get, S n = + + + + + [ ) ] [ ) ] [ )] [ )) ] [ ) ] [ [ ) ] ( n terms) S n = [ ) ] ⇒ S n =