$\large 1,2,3,\ldots,100$

Above shows the first 100 positive integers . Find the sum of all these numbers.

The answer is 5050.

**
This section requires Javascript.
**

You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.

$1+2+3+ \ldots+100\\ =\displaystyle \sum_{n=1}^{100} n\\ =\dfrac{100(101)}{2}\\ =50(101)\\ =\boxed{5050}$

Alternate method:

$1+2+3+ \ldots + 100$ is a sum of an arithmetic progression with

$a=1,\;d=1,\;n=100,\;T_n = 100$

Apply the formula for sum of arithmetic progressions:

$S_n = \dfrac{n}{2} (a+T_n)\\ S_{100} = \dfrac{100}{2} (1+100) = 50(101) = \boxed{5050}$