神马作文网如果有理数a,b满足|ab-2|+(1-b)=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1
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如果有理数a,b满足|ab-2|+(1-b)=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1+(a+2003)(b+2003)的值
ab-2=0 ,1-b=0
则,a=2 ,b=1
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2003)(b+2003)
=1/(1×2)+1/(2×3)+1/(3×4)+...+1/(2004×2005)
=1-1/2+1/2-1/3+1/3-1/4+...+1/2004-1/2005
=1-1/2005
=2004/2005
则,a=2 ,b=1
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2003)(b+2003)
=1/(1×2)+1/(2×3)+1/(3×4)+...+1/(2004×2005)
=1-1/2+1/2-1/3+1/3-1/4+...+1/2004-1/2005
=1-1/2005
=2004/2005
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