How can we calculate a sum of impare consecutive numbers starting with one?

One day, a maths teacher wanted to keep his class quiet for an hour. So he asked them to calculate the sum of the first 1000 numbers. This is, of course, a near-impossible task when done in the obvious way. (Calculators weren't invented yet.) But one bright student announced that the answer was 500500. The teacher, skeptical about this bold claim, asked how the student could have known so quickly. So the student wrote on the blackboard:

x = 1 + 2 + ..... + 1000

x = 1000+ 999 + ..... + 1

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2x = 1001+1001+ ..... + 1001

Therefore 2x = 1000 * 1001 = 1001000

That student later grew up into a prominent mathematician. His name was Carl Friedrich Gauss.

* May not be true