In honor of Carl Gauss [No Calc!]

Algebra Level 1

What is

$\large1+2+3+4+5+\cdots+98+99+100=?$

$\large\sum_{n=1}^{100} n=?$

$\text{Do not use a calculator, not even} \, \Large\color{#3D99F6}{\text{G}}\color{#D61F06}{\text{o}}\color{#CEBB00}{\text{o}}\color{#3D99F6}{\text{g}}\color{#20A900}{\text{l}}\color{#D61F06}{\text{e}}\color{#333333}{!}$

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