Sum of first n numbers

OBJECTIVE

To verify the sum of first n natural number is 1/2× n(n+1)

PREREQUISITE KNOWLEDGE

Concept of natural numbers

Area of rectangle

MATERIALS REQUIRED

White chart paper

Geometry box

Colours

Squared paper...etc

PROCEDURE

1.The sum of first n natural numbers is 

        1+2+3+4........n

2. First take a squared paper and paste it on the white chart paper

3.Mark the squares as 1,2,3.....n along the vertical lines (Y-axis) and 

  mark the squares as 1,2,3.....n+1  along the horizontal lines(X-axis) ( Image -1)

                                                                        Image1

4.Colour/shade  rectangular strips of size 1cm×1cm, 1cm×2cm, 

    1cm×3cm........1cm×n cm

5.Count the shaded squares and total number of square boxes.

OBSERVATION

1.Total shaded squares=   1/2  × Total numbers of squares

Total shaded squares=1+2+3......n

Total numbers of squares=n(n+1) 

Therefore 1+2+3.....n = 1/2 × n(n+1)

CONCLUSION

Sum of first n natural numbers is

                          = 1/2 × n(n+1)