Hello,
[tex]s=1+2+3+...+1000+1001=\sum_{i=1}^{1001}\ i \ (1) \\
s=1001+1000+...+3+2+1=\sum_{j=1}^{1001}\ 1002-j \ (2)\\
(1)+(2)==\textgreater \ 2*s=(1+1001)+(2+1000)+...+(1000+2)+(1001+1)\\
=1002*1001=(\sum_{i=1}^{1001}\ i )\ +(\sum_{i=1}^{1001}\ 1002-i )\ \\
=\sum_{i=1}^{1001}\ ( i+1002-i)\ = \sum_{i=1}^{1001}\ 1002=1001*1002\\
So\ s= \dfrac{1001*1002}{2} =501501\\
[/tex]
