(1+2+3+4+····+1999+2000+1999+···+2+1)÷2000

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(1+2+3+4+····+1999+2000+1999+···+2+1)÷2000
(1+2+3+4+····+1999+2000+1999+···+2+1)÷2000

(1+2+3+4+····+1999+2000+1999+···+2+1)÷2000
(1+2+3+4+····+1999+2000+1999+···+2+1)÷2000
=[2*(1+2+3+4+····+1999)+2000]/2000
=[(1+1999)*1999+2000]/2000
=(2000*2000)/2000
=2000

1+2+…+1999=(1+1999)×1999÷2=2000×1999÷2。这样,左边就等于2000×1999÷2+2000+2000×1999÷2=2000×2000。所以答案等于2000

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