Geometry

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What is an equation I can use to find the sum of the first 1000 counting numbers? I have been trying to find out how to figure out this problem, but can't find it my notes. Thanks in advance. :)

  • Geometry -

    The famous mathematician Carl Friedrich Gauss solved this problem when he was in elementary school, but with disastrous consequences. The teacher asked the class to add the numbers from 1 to 100, probably hoping to have peace for half an hour or so. Little Gauss finished it in about 10 seconds and went outside to play. He got reprimanded by the teacher for being lazy even though he got the answer right.

    This is what he did:
    He wrote the numbers forwards on one line, and the numbers backwards on the next line, like:
    1, 2, 3, 4, 5, 6, ...
    100, 99, 98, 97, 96, ...
    He sees that the vertical pairs always add up to 101, and there are 50 pairs of them. So the sum was evidently 5050.
    Can you continue with your problem?

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