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:
- What is the sum of first 50 natural numbers?
- What is the sum of natural numbers between 60 and 80?
- What is the sum of first 100 multiples of 4?
- What is the sum of first 60 multiples of 9?