搜搜做题作业网如果有理数a,b满足 |ab-2|+(1-b)^2=0,
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如果有理数a,b满足 |ab-2|+(1-b)^2=0,
如果有理数a,b满足 |ab-2|+(1-b)^2=0,试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+1/(a+3)(b+3)+.+1/（a+2007)(b+2007)的值.此题有规律可循吗?
如果有理数a,b满足 |ab-2|+(1-b)^2=0,试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+1/(a+3)(b+3)+.+1/（a+2007)(b+2007)的值.此题有规律可循吗?
|ab-2|+（1-b）^2=0
∴ab-2=0
1-b=0
∴a=2
b=1
∴1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2007)(b+2007）
=1/1×2+1/2×3+1/3×4+1/4×5+……+1/2008×2009
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/2008-1/2009
=1-1/2009
=2008/2009
∴ab-2=0
1-b=0
∴a=2
b=1
∴1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2007)(b+2007）
=1/1×2+1/2×3+1/3×4+1/4×5+……+1/2008×2009
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/2008-1/2009
=1-1/2009
=2008/2009
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