如果√(a-1)+(ab-2)²=0,那么1÷ab + 1÷[(a+1)(b+1)] + 1÷[(a+2)(b+2)]+...+ 1÷[(a+2007)(b+2007)]
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 05:45:50
![如果√(a-1)+(ab-2)²=0,那么1÷ab + 1÷[(a+1)(b+1)] + 1÷[(a+2)(b+2)]+...+ 1÷[(a+2007)(b+2007)]](/uploads/image/z/5612518-46-8.jpg?t=%E5%A6%82%E6%9E%9C%E2%88%9A%EF%BC%88a-1%29%2B%28ab-2%29%26sup2%3B%3D0%2C%E9%82%A3%E4%B9%881%C3%B7ab+%2B+1%C3%B7%5B%28a%2B1%29%28b%2B1%29%5D+%2B+1%C3%B7%5B%28a%2B2%29%28b%2B2%29%5D%2B%EF%BC%8E%EF%BC%8E%EF%BC%8E%2B+1%C3%B7%5B%28a%2B2007%29%28b%2B2007%29%5D)
如果√(a-1)+(ab-2)²=0,那么1÷ab + 1÷[(a+1)(b+1)] + 1÷[(a+2)(b+2)]+...+ 1÷[(a+2007)(b+2007)]
如果√(a-1)+(ab-2)²=0,那么1÷ab + 1÷[(a+1)(b+1)] + 1÷[(a+2)(b+2)]+...+ 1÷[(a+2007)(b+2007)]
如果√(a-1)+(ab-2)²=0,那么1÷ab + 1÷[(a+1)(b+1)] + 1÷[(a+2)(b+2)]+...+ 1÷[(a+2007)(b+2007)]
由√(a-1)+(ab-2)²=0知a=1,ab=2(因为两个式子都是大于等于0的数,而相加为0,那么它们只能为0)
所以a=1,b=2
代入得:1/2+1/(2*3)+1/(3*4)+.+1/(2008*2009)
注意到:1/(2*3)=1/2-1/3
1/(3*4)=1/3-1/4
.
所以原式=1/2+1/2-1/3+1/3-1/4+.+1/2008-1/2009
=1-1/2009=2008/2009