用错位相减法算 (1)3+9+27+81+243+729+2187的和
问题描述:
用错位相减法算 (1)3+9+27+81+243+729+2187的和
答
设,sn=3+9+27+81+243+729+2187
3sn=9+27+81+243+729+2187+2187*3
3sn-sn=-3+2187*3
sn=(2187*3-3)/2
答
3+9+27+81+243+729+2187
=(3+2187)+(9+81)+(27+243)+729
=2190+90+270+729
=2280+999
=3279