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