Scribd
Upload
85 views2 pages

Activity 3 AP

The document outlines a procedure to verify the formula for the sum of the first n natural numbers, which is n(n + 1)/2. It includes necessary materials, a step-by-step guide for using squared paper to visualize the sum, and observations confirming the formula's validity. The activity aims to enhance students' understanding of the concept through practical application.

Uploaded by

bansalishaan26
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
85 views2 pages

Activity 3 AP

The document outlines a procedure to verify the formula for the sum of the first n natural numbers, which is n(n + 1)/2. It includes necessary materials, a step-by-step guide for using squared paper to visualize the sum, and observations confirming the formula's validity. The activity aims to enhance students' understanding of the concept through practical application.

Uploaded by

bansalishaan26
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 2

Topie Sum of first n natural numbers.

n(n + 1l)
Objeetive To verify that the sum of the first n natural numbers is 2
n(n + 1)
ie. 1 + 2 +3 + 4 + 5 + ..... + n =
2
Pre-acquired The concepts of natural numbers.
knowledge The fornmulae for the area of a rectangle and a square.
Materials required : Centimetre squared paper, glazed paper, sheet of white paper,
pencil, ruler and a glue.
Procedure Let us consider the sum of natural numbers from 1to 10. i.e.
1+ 2 +3 + 4 + 5 + ..... + 9 + 10. Here n = 10 and n +1= 11.
1. Take a squared paper of size 10 x 11 squares and paste it
on the sheet of a white paper.
2. On the vertical line, mark the squares by 1, 2, 3, 4, 5,
10 and on the horizontal line mark the squares by 1, 2, 3,
4, 5, ...., 10, 11.
3. Cut out the rectangular strips of width 1cm each of glaze
paper of lengths equal to 1 cm, 2 cm, 10 cm and paste
them as shown in Fig. 4.1.

n= 10
B
1 2 3 4 5 6 7 10 n+l=11
Figure 4.1
Observation
ne coloured area is one half of the whole area of the squared
paper. To check this, cut the coloured area and place 1t on
the remaining of the squared paper as shown in Fig. 4.2. The
students will find that it completely covers the squared paper.

Figure 4.2

11 cm?
Area of the whole squared paper is 10 x
Area of the coloured area is -(10 × 11) cm2
2
This verifies that for n = 10.
n(n + 1)
.. n=
2
for
The students develop a geometrical intuition of the formula
Learning outcomes : starting from 1.
the sum of natural numbers
activity
The teacher can ask the students to perform the above
Result verifies the same.
for any other value of n and thus

You might also like