Use the approach in Gauss's Problem to find the following

logosomatw 2022-01-23 Answered
Use the approach in Gausss
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nebajcioz
Answered 2022-01-24 Author has 15 answers
Consider the series 1+2+3+4++1001.
For the series 1+2+3+4++1001, it is clear that there are 1001 terms, which is odd.
So, add the series to itself in reverse order.
Note that each pair has a sum of 1002 and there are 1001 pairs which gives:
1002(1001)=1003002
Since this is the sum of the series added to itself, the sum of the original series is half this sum.
The sum of 1+2+3+4++1001 is then 12(1003002)=501501
This is the answer.
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