已知集合M={X/1小于等于X小于等于10,X属于N},对它的非空子集A,将A中每个元素K都乘以(-1)K次方在求和,如:A={1,3,6},可求得和为(-1)X1+(-1)3次方X3+(-1)6次方X6=2,则对M的所有非空子集,求这些和的
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/28 20:00:40
![已知集合M={X/1小于等于X小于等于10,X属于N},对它的非空子集A,将A中每个元素K都乘以(-1)K次方在求和,如:A={1,3,6},可求得和为(-1)X1+(-1)3次方X3+(-1)6次方X6=2,则对M的所有非空子集,求这些和的](/uploads/image/z/1972142-62-2.jpg?t=%E5%B7%B2%E7%9F%A5%E9%9B%86%E5%90%88M%3D%7BX%2F1%E5%B0%8F%E4%BA%8E%E7%AD%89%E4%BA%8EX%E5%B0%8F%E4%BA%8E%E7%AD%89%E4%BA%8E10%2CX%E5%B1%9E%E4%BA%8EN%7D%2C%E5%AF%B9%E5%AE%83%E7%9A%84%E9%9D%9E%E7%A9%BA%E5%AD%90%E9%9B%86A%2C%E5%B0%86A%E4%B8%AD%E6%AF%8F%E4%B8%AA%E5%85%83%E7%B4%A0K%E9%83%BD%E4%B9%98%E4%BB%A5%EF%BC%88-1%EF%BC%89K%E6%AC%A1%E6%96%B9%E5%9C%A8%E6%B1%82%E5%92%8C%2C%E5%A6%82%EF%BC%9AA%3D%7B1%2C3%2C6%7D%2C%E5%8F%AF%E6%B1%82%E5%BE%97%E5%92%8C%E4%B8%BA%EF%BC%88-1%EF%BC%89X1%2B%28-1%293%E6%AC%A1%E6%96%B9X3%2B%28-1%296%E6%AC%A1%E6%96%B9X6%3D2%2C%E5%88%99%E5%AF%B9M%E7%9A%84%E6%89%80%E6%9C%89%E9%9D%9E%E7%A9%BA%E5%AD%90%E9%9B%86%2C%E6%B1%82%E8%BF%99%E4%BA%9B%E5%92%8C%E7%9A%84)
已知集合M={X/1小于等于X小于等于10,X属于N},对它的非空子集A,将A中每个元素K都乘以(-1)K次方在求和,如:A={1,3,6},可求得和为(-1)X1+(-1)3次方X3+(-1)6次方X6=2,则对M的所有非空子集,求这些和的
已知集合M={X/1小于等于X小于等于10,X属于N},对它的非空子集A,将A中每个元素K都乘以(-1)K次方在求和,如:A={1,3,6},可求得和为(-1)X1+(-1)3次方X3+(-1)6次方X6=2,则对M的所有非空子集,求这些和的总和.
已知集合M={X/1小于等于X小于等于10,X属于N},对它的非空子集A,将A中每个元素K都乘以(-1)K次方在求和,如:A={1,3,6},可求得和为(-1)X1+(-1)3次方X3+(-1)6次方X6=2,则对M的所有非空子集,求这些和的
M={x| 1≤x≤10,x∈N }
= { 1,2,3,4,5,6,7,8,9 }
number of non empty subset of M = 2^9 -1
= 511
9C1+9C2+9C3+...+9C9 = 511
number of elements in all those non-empty subset of M
= (1)9C1 + (2)9C2+(3)9C3+...+(9)9C9
= 9 + 2(36) + 3(84)+4(126)+5(126)+6(84)+7(36)+8(9) +9(1)
= 9 +72+ 252+ 504+ 630+ 504+ 252+72+9
= 2304
Number of "1" appears in all those non-empty subet
=Number of "2" appears in all those non-empty subet
=...
=Number of "9" appears in all those non-empty subet
=2304/9 = 256
和的总和
=256( -1+2 - 3 +4 -5+6-7+8-9)
= 256(-5)
= -1280
答案是2560