Question

By graphical method verify that the sum of first n natural numbers is (+1)/2.​

Answer 1

Step-by-step explanation:

Math Labs with Activity – Sum of the First n Natural Numbers

January 18, 2018 by Prasanna

Math Labs with Activity – Sum of the First n Natural Numbers

OBJECTIVE

To verify by a graphical method that the sum of the first ti natural numbers is



Materials Required

A sheet of white paper

A geometry box

A tube of glue

A long, colored paper tape of uniform width (say, 1 unit)

A pencil

Theory

The sum of the first n terms of an AP is given by

 ….(i)

Taking a = 1 and d = 1, the AP becomes 1,2, 3, 4, …

∴ putting a =1 and d = 1 in equation (i), we get



i.e., the sum of the first n natural numbers =



Procedure

Step 1: We shall verify the formula for the first 10 natural numbers, i.e., for n = 10.

Step 2: Draw horizontal and vertical lines on the sheet of white paper to mark squares, each of size 1 unit x 1 unit.

Step 3: Cut the colored paper tape in 10 rectangular strips of lengths 1 unit, 2 units, 3 units, …, 10 units.

Step 4: Paste these strips on the grid sequentially as shown in Figure 4.1.

Step 5: Complete the rectangle ABCD so that AB = 11 units and BC = 10 units.



Step 6: Cut the portion of the rectangle ABCD which is covered by the colored paper strips. We find that this portion completely covers the remaining portion of the rectangle ABCD