# Sum to n terms of Special Series

Let us find the values (formula of (1), (2) and (3)

This is an A.P with .

Adding vertically both sides,

(3) Let

Let us consider the pattern:

**Note:**

All the formulae for can be proved by mathematical induction.

**Example 1:**

Find the sum to terms of the series whose term is

**Solution:**

**Example 2:**

Find the sum of 20 terms of the series

**Solution:**

term of the series

=(term of the A.P 1,2,3,..) (term of the series )

**Example 3:**

Find the sum to terms of the series 3+7+13+21+31+............

**Solution:**

Subtracting

**Example 4:**

Find the sum to n terms of the series :

**Solution:**

adding vertically,