1²-3²+5²-7²+9²-11²+...+49²-51²
来源:学生作业学帮网 编辑:学帮网 时间:2024/06/05 08:21:33
1²-3²+5²-7²+9²-11²+...+49²-51²
=(1+3)(1-3)+(5+7)(5-9)+……+(49+51)(49-51)
=(1+3)×(-2)+(5+7)×(-2)+……+(49+51)×(-2)
=(1+3+5+7+……+49+51)×(-2)
=(1+51)×26/2×(-2)
=-1352
原式=(1-3)*(1+3)+(5-7)*(5+7).....+(49-51)*(49+51)
=-2*(4+12+20+....+92+100)
=-2*(4+100)*13/2
=-1352