若|ab-2|+|b-1|=0,试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+···+1/(a+2010)(b+2010)的值若|ab-2|+|b-1|=0,试求1/ab加1/(a+1)(b+1)加1/(a+2)(b+2)+···加1/(a+2010)(b+2010)的值,8号要交了,救命啊
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/30 07:48:48
![若|ab-2|+|b-1|=0,试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+···+1/(a+2010)(b+2010)的值若|ab-2|+|b-1|=0,试求1/ab加1/(a+1)(b+1)加1/(a+2)(b+2)+···加1/(a+2010)(b+2010)的值,8号要交了,救命啊](/uploads/image/z/10321815-39-5.jpg?t=%E8%8B%A5%7Cab-2%7C%2B%7Cb-1%7C%3D0%2C%E8%AF%95%E6%B1%821%2Fab%2B1%2F%28a%2B1%29%28b%2B1%29%2B1%2F%28a%2B2%29%28b%2B2%29%2B%C2%B7%C2%B7%C2%B7%2B1%2F%28a%2B2010%29%28b%2B2010%29%E7%9A%84%E5%80%BC%E8%8B%A5%7Cab-2%7C%2B%7Cb-1%7C%3D0%2C%E8%AF%95%E6%B1%821%2Fab%E5%8A%A01%2F%28a%2B1%29%28b%2B1%29%E5%8A%A01%2F%28a%2B2%29%28b%2B2%29%2B%C2%B7%C2%B7%C2%B7%E5%8A%A01%2F%28a%2B2010%29%28b%2B2010%29%E7%9A%84%E5%80%BC%2C8%E5%8F%B7%E8%A6%81%E4%BA%A4%E4%BA%86%2C%E6%95%91%E5%91%BD%E5%95%8A)
若|ab-2|+|b-1|=0,试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+···+1/(a+2010)(b+2010)的值若|ab-2|+|b-1|=0,试求1/ab加1/(a+1)(b+1)加1/(a+2)(b+2)+···加1/(a+2010)(b+2010)的值,8号要交了,救命啊
若|ab-2|+|b-1|=0,试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+···+1/(a+2010)(b+2010)的值
若|ab-2|+|b-1|=0,试求1/ab加1/(a+1)(b+1)加1/(a+2)(b+2)+···加1/(a+2010)(b+2010)的值,8号要交了,救命啊
若|ab-2|+|b-1|=0,试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+···+1/(a+2010)(b+2010)的值若|ab-2|+|b-1|=0,试求1/ab加1/(a+1)(b+1)加1/(a+2)(b+2)+···加1/(a+2010)(b+2010)的值,8号要交了,救命啊
由题意得
ab-2=0
b-1=0
得a=2,b=1
后式可化成
1/b-1/a+1/(b+1)-1/(a+1)+…………+1/(b+2010)-1/(a+2010)
=1-1/2+1/2-1/3+1/3-1/4+………………+1/2011-1/2012
=1-1/2012
=2011/2012
|ab-2|+|b-1|=0 -->ab=2,b=1 -->a=2
1/(1*2)+1/(2*3)+1/(3*4)+……+1/(2011*2012)裂项得
1/1-1/2+1/2-1/3+……+1/2011-1/2012=1-1/2012=2011/2012
2011/2012
a=2,b=1
原式=1/2+1/3*2+1/4*3+···+1/2012*2011=1/2+1/2-1/3+1/3-1/4+···+1/2010-1/2011+1/2011-1/2012