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This has been mentioned before but here is a video and motivation of Gauss proof

Gauss proof for the sum of first 100 natural numbers

There is more videos in that side site that include proofs

here is the list of instructional videos from isallaboutmath.com

especially this one

Proof (stereographic projection)

this should be accessible with the most basic geometric knowledge.

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This has been mentioned before but here is a video and motivation of Gauss proof

Gauss proof for the sum of first 100 natural numbers

There is more videos in that side that include proofs

here is the list of instructional videos from isallaboutmath.com

especially this one

Proof (stereographic projection)

this should be accessible with the most basic geometric knowledge.