Page 29 - Mathematics Class - X

OBSERVATIONS
The shaded area is one half of the whole area of the graph paper taken. To see it, cut the shaded portion and place
it on the remaining part of the grid. The student will observe that it completely superimposes the grid.

Area of the whole graph paper is 10 × 11 cm 2

Area of the shaded portion is (10 × 11) cm 2
2
This verifies that, for n = 10,

n (n + 1)
sum of first n natural numbers, ∑n =
2

The same verification can be done for any other value of n.

INFERENCE

This experiment shows that we can find the sum of natural numbers starting from one with the help of a formula.

EXTENDED TASK

1. Verify that the sum of first n even numbers is n(n + 1) experimentally.

2. Numbers in mathematics are inevitable and they do form a pattern. Find any 5 such famous series and
discuss in groups about their unique features.

[Hint: Explore the famous Pascal’s triangle to identify the series.]

APPLICATION

1. This is useful in researches related to larger natural numbers.

2. Result can be used to find the sum of first n terms of the list of numbers:

(i) 12, 22, 32, ...

(ii) 13, 23, 33, ...

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