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Gauss's Pairing Trick (Rainbow Idea)

Idea · Beginner

Problem Solving

Pair up the elements:

Gauss pairing trick using rainbow arcs to pair terms

or

S=1+2+3+⋯+98+99+100 S=1+2+3+\cdots+98+99+100
S=100+99+98+⋯+3+2+1 S=100+99+98+\cdots+3+2+1
2S=101+101+⋯+101 2S=101+101+\cdots+101
2S=100×101 2S=100\times101

Therefore:

S=100×1012 S=\frac{100\times101}{2}
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