已知|ab-2|与|b-1|互为相反数,试求下列代数式的值1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2008)(b+2008)
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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1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2008)(b+2008)](/uploads/image/z/3035787-51-7.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%BC1%2Fab%2B1%2F%28a%2B1%29%28b%2B1%29%2B1%2F%28a%2B2%29%28b%2B2%29%2B.%2B1%2F%28a%2B2008%29%28b%2B2008%29)
已知|ab-2|与|b-1|互为相反数,试求下列代数式的值1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2008)(b+2008)
已知|ab-2|与|b-1|互为相反数,试求下列代数式的值
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2008)(b+2008)
已知|ab-2|与|b-1|互为相反数,试求下列代数式的值1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2008)(b+2008)
|ab-2|与|b-1|互为相反数
ab-2=0,b-1=0
a=2,b=1
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2008)(b+2008)
=1/2*1+1/3*2+1/4*3+...+1/2010*2009
=1-1/2+1/2-1/3+1/3-1/4+...+1/2009-1/2010
=1-1/2010
=2009/2010
因为|ab-2|与|b-1|互为相反数,
所以|ab-2|+|b-1|=0.
所以ab-2=0,b-1=0.
所以a=2,b=1.
所以原式=1/1*2+1/2*3+...+1/2009*2010
=1-1/2+1/2-1/3+1/3-1/4+1/4+...+1/2003-1/2010
=1-1/2010
=2009/2010.
|ab-2|与|b-1|互为相反数
所以|ab-2|+|b-1|=0
绝对值大于等于0,相加等于0,若有一个大于0,则另一个小于0,不成立。
所以两个都等于0
所以ab-2=0,b-1=0
b=1,ab=2,所以a=2/b=2
所以
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+......+1/(a+2008)(b+2008...
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|ab-2|与|b-1|互为相反数
所以|ab-2|+|b-1|=0
绝对值大于等于0,相加等于0,若有一个大于0,则另一个小于0,不成立。
所以两个都等于0
所以ab-2=0,b-1=0
b=1,ab=2,所以a=2/b=2
所以
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+......+1/(a+2008)(b+2008)
=1/1*2+1/2*3+……+1/2009*2010
=(1/1-1/2)+(1/2-1/3)+……+(1/2009-1/2010)
=1-1/2010
=2009/2010
收起
|ab-2|+|b-1|=0
而绝对值又是非负,则b=1,ab=2,所以a=2
原式
=1/1*2+1/2*3+1/3*4+……+1/2009*2010
=1-1/2+1/2-1/3+1/3-1/4+……+1/2009-1/2010
=1-1/2010
=2009/2010
ab-2|与|b-1|互为相反数
ab-2=0,b-1=0
a=2,b=1
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+......+1/(a+2008)(b+2008)
=1/2*1+1/3*2+1/4*3+...+1/2010*2009
=1-1/2+1/2-1/3+1/3-1/4+...+1/2009-1/2010
=1-1/2010
=2009/2010