# How do you find the sum of the first 5000 natural numbers?

Jul 2, 2016

The sum of the first $n$ positive integers, $n$ being a natural number, is given by ${S}_{n} = \frac{n \left(n + 1\right)}{2}$.

${S}_{5000} = \frac{5000 \left(5001\right)}{2}$

${S}_{5000} = \text{12 502 500}$

Hopefully this helps!

Jul 2, 2016

12502500

#### Explanation:

Without using formula we can proceed as follows.

Let the sum be S then

$S = 1 + 2 + 3 + 4 + 5 + - - - 4998 + 4999 + 5000. \ldots \left(1\right)$

Again writing in reverse order

$S = 5000 + 4999 + 4998 + - - - - + 3 + 2 + 1. \ldots . . \left(2\right)$

$2 S = \left(5000 + 1\right) + \left(4999 + 2\right) \text{+} - - + \left(4999 + 2\right) + \left(5000 + 1\right)$

$S = \frac{5000 \times 5001}{2} = 12502500$