求和:(a-1)+(a2-2)+…+(an-n),(a≠0)
问题描述:
求和:(a-1)+(a2-2)+…+(an-n),(a≠0)
答
原式=(a+a2+…+an)-(1+2+…+n)
=(a+a2+…+an)-
n(n+1) 2
=
−a(1−an) 1−a
,a≠1n(n+1) 2
,a=1n−n2
2