[n+(n+1)+(n+2)+……+1]化简

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[n+(n+1)+(n+2)+……+1]化简[n+(n+1)+(n+2)+……+1]化简[n+(n+1)+(n+2)+……+1]化简错了吧是n+(n-1)+(n-2)+……+1令S=n+(n-1)+(

[n+(n+1)+(n+2)+……+1]化简
[n+(n+1)+(n+2)+……+1]化简

[n+(n+1)+(n+2)+……+1]化简
错了吧
是n+(n-1)+(n-2)+……+1
令S=n+(n-1)+(n-2)+……+1
则S=1+2+3+……+n
相加
2S=(n+1)+[(n-1)+2]+……+(1+n)
=(n+1)+(n+1)+……+(n+1)
=n(n+1)
所以原式=S=n(n+1)/2