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

1 answer:

kramer3 years ago

5 0

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= \dfrac{1001*1002}{2} =501501\\
 




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