1 to 100

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

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:

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

The answer is easily obtained via Gauss's summation trick. $\frac{1}{2}\times100\times101 = 5050$

Answer is $\dfrac{100 × 101}{2} = \color{#69047E}{\boxed{5050}}$ .