(-1)x(-2)x(-3)+(-2)x(-3)x(-4)+……+(-100)x(-101)x(-102)
题目
(-1)x(-2)x(-3)+(-2)x(-3)x(-4)+……+(-100)x(-101)x(-102)
答案
令Sn=1*2*3+2*3*4+.+n*(n+1)(n+2)
=1/4[(1*2*3*4-0*1*2*3)+(2*3*4*5-1*2*3*4)+.+
n(n+1)(n+2)(n+3)-(n-1)n(n+1)(n+2)]
=1/4*n(n+1)(n+2)(n+3)
(-1)x(-2)x(-3)+(-2)x(-3)x(-4)+……+(-100)x(-101)x(-102)
=-S100
=-1/4x100x101x102x103=-26527650
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