神马作文网求19^3+20^3+21^3+…28^3的值
来源：学生作业帮 编辑：神马作文网作业帮 分类：数学作业 时间：2024/11/13 02:01:58
求19^3+20^3+21^3+…28^3的值
19³+20³+21³+…28³
=19³+28³+20³+27³+.
=(19+28)(19²-19*28+28²)+(20+27)(20²-20*27+27²)+(21+26)(21²-21*26+26²)+.
=47(19²-19*28+28²+20²-20*27+27²+21²-21*26+26²+.)
=47(19²-2*19*28+28²+19*28+20²-2*20*27+27²+20*27+21²-2*21*26+26²+21*26+.)
=47(9²+19*28+7²+20*27+5²+21*26+...)
=47[9²+7²+5²+3²+1²+19*28+(19+1)（28-1）+(19+2)（28-2）+...]
=47(165+19*28+19*28+19-28-1+19*28+2*19-2*28-4+.]
=47(165+5*19*28-7-2*7-3*7-4*7-1-4-9-16]
=47(165+2660-70-30)
=47*2725
=128075
=19³+28³+20³+27³+.
=(19+28)(19²-19*28+28²)+(20+27)(20²-20*27+27²)+(21+26)(21²-21*26+26²)+.
=47(19²-19*28+28²+20²-20*27+27²+21²-21*26+26²+.)
=47(19²-2*19*28+28²+19*28+20²-2*20*27+27²+20*27+21²-2*21*26+26²+21*26+.)
=47(9²+19*28+7²+20*27+5²+21*26+...)
=47[9²+7²+5²+3²+1²+19*28+(19+1)（28-1）+(19+2)（28-2）+...]
=47(165+19*28+19*28+19-28-1+19*28+2*19-2*28-4+.]
=47(165+5*19*28-7-2*7-3*7-4*7-1-4-9-16]
=47(165+2660-70-30)
=47*2725
=128075