Question

Use​ Gauss's approach to find the following sums​ (do not use​ formulas).
1+3+5+7+...+1001

Answer 1

Hello,


`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= (1001*1002)/(2) =501501\\`