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06 December, 2007

Activity Sum of first n natural numbers

Aim : To verify that the sum of first n natural numbers is n (n + 1) / 2, i.e. Σ n = n (n + 1) / 2, by graphical method. Material Required : Coloured paper,squared paper, sketch pen ,ruler Procedure: Let us consider the sum of natural numbers say from 1 to 10, i.e. 1 + 2 + 3 + … + 9 + 10. Here n = 10 and n + 1 = 11. 1. Take a squared paper of size 10 × 11 squares and paste it on a chart paper. 2. On the left side vertical line, mark the squares by 1, 2, 3, … 10 and on the horizontal line, mark the squares by 1, 2, 3 …. 11. 3. With the help of sketch pen, shade rectangles of length equal to 1 cm, 2 cm, …, 10cm and of 1 cm width each.

Observations: The shaded area is one half of the whole area of the squared paper taken. To see this, cut the shaded portion and place it on the remaining part of the grid. It is observed that it completely covers the grid. Area of the whole squared paper is 10 × 11 cm2

Area of the shaded portion is (10 × 11) / 2 cm2

This verifies that, for n = 10, Σ n = n × (n + 1) / 2 The same verification can be done for any other value of n.

Answer the following after doing this activity:

  1. What is the sum of first 50 natural numbers?

  2. What is the sum of natural numbers between 60 and 80?

  3. What is the sum of first 100 multiples of 4?

  4. What is the sum of first 60 multiples of 9?


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Anonymous said...

thanx a lottt,it was a great help:)

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Anonymous said...

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:* sumit royal bengali

Anonymous said...

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Anonymous said...

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rohan verma said...

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Anonymous said...

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