(1\2+1\3+•••+1\2008)*(1+1\2+•••+1\2007)-(1+1\2+•••+1\2008)*(1\2+1\3+•••+1\2007)
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/02 17:26:16
![(1\2+1\3+•••+1\2008)*(1+1\2+•••+1\2007)-(1+1\2+•••+1\2008)*(1\2+1\3+•••+1\2007)](/uploads/image/z/8209055-47-5.jpg?t=%281%5C2%2B1%5C3%2B%26%238226%3B%26%238226%3B%26%238226%3B%2B1%5C2008%29%2A%EF%BC%881%2B1%5C2%2B%26%238226%3B%26%238226%3B%26%238226%3B%2B1%5C2007%EF%BC%89-%EF%BC%881%2B1%5C2%2B%26%238226%3B%26%238226%3B%26%238226%3B%2B1%5C2008%EF%BC%89%2A%EF%BC%881%5C2%2B1%5C3%2B%26%238226%3B%26%238226%3B%26%238226%3B%2B1%5C2007%EF%BC%89)
(1\2+1\3+•••+1\2008)*(1+1\2+•••+1\2007)-(1+1\2+•••+1\2008)*(1\2+1\3+•••+1\2007)
(1\2+1\3+•••+1\2008)*(1+1\2+•••+1\2007)-
(1+1\2+•••+1\2008)*(1\2+1\3+•••+1\2007)
(1\2+1\3+•••+1\2008)*(1+1\2+•••+1\2007)-(1+1\2+•••+1\2008)*(1\2+1\3+•••+1\2007)
令a=1\2+1\3+•••+1\2007
则原式=(a+1/2008)(1+a)-(1+a+1/2008)a
=a(1+a)+1/2008(1+a)-a(1+a)-1/2008a
=1/2008(1+a)-1/2008a
=1/2008+1/2008a-1/2008a
=1/2008