On 249th birth anniversary of Carl Friedrich Gauss.
In 1786, a teacher gave his class a problem to keep the students occupied, as they were being particularly noisy.
The task seemed simple:
add all the numbers from 1 to 100—that is,
1 2 3 … 100.
It was the kind of problem expected to keep the class busy for quite some time.
However, one student solved it almost instantly. The teacher was astonished—how could anyone arrive at the answer so quickly?
The student used a clever approach. He wrote the sequence twice: once in ascending order and once in descending order:
1 2 3 … ... ... 100
100 99 98 … 1
Then he added the corresponding terms:
(1 100), (2 99), (3 98), (4 97), and so on.
Each pair sums to 101. Since there are 100 such pairs, the total becomes:
2S = 101 × 100
Dividing both sides by 2:
S = (101 × 100) ÷ 2 = 5050
Thus, the sum of the first 100 natural numbers is 5050.
That remarkable child prodigy was Carl Friedrich Gauss.
A mind capable of such elegant insight at a young age went on to make profound contributions to mathematics and science.