如果有理数a、b满足丨a-2丨+(1-b)²=0?试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2010)(b+2010)的值.(提示:1/2×3=1/2-1/3,1/3×4=1/3-1/4^)

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如果有理数a、b满足丨a-2丨+(1-b)²=0?试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2010)(b+2010)的值.(提示:1/2×3=1/2-1/3,1/3×4=1/3-1/4^)
如果有理数a、b满足丨a-2丨+(1-b)²=0?
试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2010)(b+2010)的值.(提示:1/2×3=1/2-1/3,1/3×4=1/3-1/4^)

如果有理数a、b满足丨a-2丨+(1-b)²=0?试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2010)(b+2010)的值.(提示:1/2×3=1/2-1/3,1/3×4=1/3-1/4^)
如果有理数a、b满足丨a-2丨+(1-b)²=0
则,a-2=0 1-b=0
a=2 b=1
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2010)(b+2010)
=1/2*1+1/3*2+1/3*4+/14*5+++++++.+1/2012*2011
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.-1/2011+1/2011-1/2012
=1-1/2012
=2011/2012