1*2+2*3+3*4+4*5.999*1000
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![1*2+2*3+3*4+4*5.999*1000](/uploads/image/z/764428-4-8.jpg?t=1%2A2%2B2%2A3%2B3%2A4%2B4%2A5.999%2A1000)
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1*2+2*3+3*4+4*5.999*1000
1*2+2*3+3*4+4*5.999*1000
1*2+2*3+3*4+4*5.999*1000
1*2+2*3+3*4+4*5.999*1000
=2^2-2+3^2-3+4^2-4+.+1000^2-1000
=1^2+2^2+3^2+.+1000^2 -(1+2+3+.1000)
=1000(1000+1)(2*1000+1)/6 -1000(1000+1)/2
=1000(1000+1)(2001/6-1/2)
=333333000
=1*1+2*2+3*3+…+999*999+1+2+3+…+999