Ahmad Asaad

Mathematics is essential to our understanding the invisible patterns of the universe. In 1623, Galileo wrote,

"The great book of nature can be read only by those who know the language in which it was written. And this language is mathematics."

— Keith Devlin. Introduction to Mathematical Thinking

Summation of the $n$ natural numbers from $1$ to $n$ can be calculated using this formula:

$$ \sum_{i=1}^{n}i = \frac{n(n+1)}{2} $$

and this formula is the same formula used for calculating the $n$th triangular number:

$$ T_n = \frac{n(n+1)}{2} $$

For example:

• $ T_1 = \frac{1(1+1)}{2} = 1 $
• $ T_2 = \frac{2(2+1)}{2} = 1 + 2 = 3 $
• $ T_3 = \frac{3(3+1)}{2} = 1 + 2 + 3 = 6 $