Question

cat face 1+3+5+.....+1997

Answer 1

$\displaystyle 1+3+5+...+1997 \\ 1997=1+(n-1) \cdot 2 \\ 1997=1+2n-2 \\ 2n=1997-1+2 \\ 2n=1998 \\ n=1998:2 \\ n=999 \\ S_{999}= \frac{2+998 \cdot 2}{2} \cdot 999 \\ \\ S_{999}= \frac{2+1996}{2} \cdot 999 \\ \\ S_{999}= \frac{1998}{2} \cdot 999 \\ \\ S_{999}=999 \cdot 999 \\ S_{999}=998001$