NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 5: Arithematic Progressions - Exercise 5.1
Question 14

Question.  14

The famous mathematician associated with finding the sum of the first 100 natural numbers is

(A)

Pythagoras

(B)

Newton

(C)

Gauss

(D)

Euclid

Detailed Answer with Explanation:

When Gauss was a small schoolboy, his teacher asked the class to add all the numbers from 1 to 100.

Instead of adding one by one, Gauss thought of a smart trick:

He paired the first and last numbers:

\(1 + 100 = 101\)

Then the second and the second-last numbers:

\(2 + 99 = 101\)

Similarly, \(3 + 98 = 101\), and so on.

He noticed that every pair adds up to 101.

There are 50 such pairs (because 100 numbers make 50 pairs).

So the total sum is:

\(50 \times 101 = 5050\)

This clever method is why Gauss is remembered for this problem.

NCERT Exemplar Solutions Class 10 – Mathematics – CHAPTER 5: Arithematic Progressions – Exercise 5.1 | Detailed Answers