Welcome to Planet Infinity KHMS

Search This Blog

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?

10 comments:

Siddhant said...

Thanks a lot for this it reeli helped!
Sid

vero y maria said...

thanks for help.
The blogger seemed to us to be super well, usefully and didactically because he presents images which facilitates the comprehension of the exposed problems, beside presenting videoes for those topics that are mas difficult to understand. The blogger presents many topics that we include in the studies of our career which undoubtedly is a help for the students and future teachers.
The blogger is of very easy access, the topics are presented in a list which makes us that the search realizes of way mas simple in addition he presents a bar of search where the person who accedes deposits the topic that searches doing mas simply to find it.

Anonymous said...

thanx a lottt,it was a great help:)

Anonymous said...

thnx

Anonymous said...

Thanxx rashmi mam u r grt.



:* sumit royal bengali

Anonymous said...

thnx sooooooooo much mam!

Anonymous said...

thanks a lot for this info...!

Anonymous said...

THANKU FOR THIS ANSWER. TO ALLLLL.

rohan verma said...

thank you for helping me

Anonymous said...

very helpfull

Recent Comments

Readers