3+7+11+15+19+23+27+------4019+4023=?的简便运算方式?
来源:学生作业帮 编辑:灵鹊做题网作业帮 分类:数学作业 时间:2024/06/17 03:58:24
3+7+11+15+19+23+27+------4019+4023=?的简便运算方式?
![3+7+11+15+19+23+27+------4019+4023=?的简便运算方式?](/uploads/image/z/6115381-61-1.jpg?t=3%2B7%2B11%2B15%2B19%2B23%2B27%2B------4019%2B4023%3D%3F%E7%9A%84%E7%AE%80%E4%BE%BF%E8%BF%90%E7%AE%97%E6%96%B9%E5%BC%8F%3F)
3+7+11+15+19+23+27+------4019+4023
=4*1-1+4*2-1+4*3-1+4*4-1+4*5-1+...+4*1006-1
=4*1+4*2+4*3+4*4+4*5+...+4*1006-1006
=4*(1+2+3+4+5+6+..+1006)-1006
=4*(1+1006+2+1005+...+503+504+505)-1006
=4*1007*503+2020-1006
=2025070
=4*1-1+4*2-1+4*3-1+4*4-1+4*5-1+...+4*1006-1
=4*1+4*2+4*3+4*4+4*5+...+4*1006-1006
=4*(1+2+3+4+5+6+..+1006)-1006
=4*(1+1006+2+1005+...+503+504+505)-1006
=4*1007*503+2020-1006
=2025070