TO FIND THE
VALUE OF a^n
(WHERE a AND
n ARE
NATURAL
NUMBERS)
USING PAPER
FOLDING
Answers
Step-by-step explanation:
The sum of the first n terms of an AP is given by
Math Labs with Activity – Sum of the First n Natural Numbers 2 ….(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
Math Labs with Activity – Sum of the First n Natural Numbers 3
i.e., the sum of the first n natural numbers =
Math Labs with Activity – Sum of the First n Natural Numbers 4
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
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