m-2m-3m+4m-5m-6m=m-2m-3m+4m-5m-6m+···+2002m-2003m-2004m

问题描述:

m-2m-3m+4m-5m-6m=
m-2m-3m+4m-5m-6m+···+2002m-2003m-2004m

= (1-2-3+4-5-6)m
= -11m

可将每三项结合算得-4m-7m-10m-……-2005m提出负号得-(4m+7m+……+2005m)此为等差数列,公差为3m,再根据等差数列求和公式【(a1+an)*3m}/2得结果。

m-2m-3m+4m-5m-6m+···+2002m-2003m-2004m
= [(1-2-3)+(4-5-6)+···(2002-2003-2004)]m
= -(4+7+11+···+2005)m
= -668*(4+2005)m/2
= -671006m
等差数列公式:
Sn=n(a1+an)/2
an=a1+(n-1)d