The Prodigy Gauss

Carl Friedrich Gauss was a German mathematician in the 18th century, sometimes referred to as the “Prince of Mathematicians” and the “greatest mathematician since antiquity”. He has had a remarkable influence in many fields of mathematics and science and is ranked as one of history’s most influential mathematicians.

Gauss was a child prodigy. There are many anecdotes concerning his precocity as a child, and he made his first ground-breaking mathematical discoveries while still a teenager. At just three years old, he corrected an error in his father payroll calculations, and he was looking after his father’s accounts on a regular basis by the age of 5.

Legend has it that when Gauss was 7 years old, his school teacher gave his class, as an exercise , the assignment to calculate  $\fn_phv \large 1 + 2 + 3 + ..............+99 +100$ thinking that it would take the students several minutes to calculate. The teacher was quite surprised when young Gauss came up with the answer almost immediately! Gauss even at age 7 recognized that there was a quick way to add consecutive integers.

This is how he did it:

$\fn_phv \large S = 1 + 2 + 3 + ..............+99 +100$

Then he wrote the sum in reverse which should also add to S.

$\fn_phv \large S = 100 + 99 + 98 + ..............+2 +1$

He noted when you add the two sums you get 101, 100 times

$\fn_phv \large 2S = 101+ 101 + .......101 + 101 \; (100\; times)$

So  $\fn_phv \large 2S = 101 \times100$

$\fn_phv \large S = 5050$