已知|ab-2|与|b-1|互为相反数,试求下列代数式的值如题,求这个代数式:1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+1/(a+3)(b+3)+…+1/(a+2008)(b+2008)对于我来说很难,谢谢了!~
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![已知|ab-2|与|b-1|互为相反数,试求下列代数式的值如题,求这个代数式:1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+1/(a+3)(b+3)+…+1/(a+2008)(b+2008)对于我来说很难,谢谢了!~](/uploads/image/z/7258152-48-2.jpg?t=%E5%B7%B2%E7%9F%A5%7Cab-2%7C%E4%B8%8E%7Cb-1%7C%E4%BA%92%E4%B8%BA%E7%9B%B8%E5%8F%8D%E6%95%B0%2C%E8%AF%95%E6%B1%82%E4%B8%8B%E5%88%97%E4%BB%A3%E6%95%B0%E5%BC%8F%E7%9A%84%E5%80%BC%E5%A6%82%E9%A2%98%2C%E6%B1%82%E8%BF%99%E4%B8%AA%E4%BB%A3%E6%95%B0%E5%BC%8F%EF%BC%9A1%2Fab%2B1%2F%28a%2B1%29%28b%2B1%29%2B1%2F%28a%2B2%29%28b%2B2%29%2B1%2F%28a%2B3%29%28b%2B3%29%2B%E2%80%A6%2B1%2F%28a%2B2008%29%28b%2B2008%29%E5%AF%B9%E4%BA%8E%E6%88%91%E6%9D%A5%E8%AF%B4%E5%BE%88%E9%9A%BE%2C%E8%B0%A2%E8%B0%A2%E4%BA%86%21%7E)
已知|ab-2|与|b-1|互为相反数,试求下列代数式的值如题,求这个代数式:1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+1/(a+3)(b+3)+…+1/(a+2008)(b+2008)对于我来说很难,谢谢了!~
已知|ab-2|与|b-1|互为相反数,试求下列代数式的值
如题,求这个代数式:
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+1/(a+3)(b+3)+…+1/(a+2008)(b+2008)
对于我来说很难,谢谢了!~
已知|ab-2|与|b-1|互为相反数,试求下列代数式的值如题,求这个代数式:1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+1/(a+3)(b+3)+…+1/(a+2008)(b+2008)对于我来说很难,谢谢了!~
∵|ab-2|≥0,|b-1|≥0
|ab-2|=-|b-1|=0
∴a=2,b=1
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+1/(a+3)(b+3)+…+1/(a+2008)(b+2008)
=1/(1*2)+1/(2*3)+...+1/(2009*2010)
=1-1/2+1/2-1/3+...+1/2008-1/2009+1/2009-1/2010
=1-1/2010
=2009/2010
b=1,a=2,最后结果为2009/2010
|ab-2|与|b-1|互为相反数
则ab-2=0,b-1=0
解得a=2,b=1
代入得
1/2*1+1/3*2+……+1/2010*2009
=1-1/2+1/2+1/3+……+1/2009-1/2010
=1-1/2010
=2009/2010
绝对值都为非负数,所以两个绝对值互为相反数,这两个绝对值都为0