如果有理数a、b满足|ab-2|+|1-b|=0,试求1 /ab+1/a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2009)(b+2009)的值
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![如果有理数a、b满足|ab-2|+|1-b|=0,试求1 /ab+1/a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2009)(b+2009)的值](/uploads/image/z/672118-70-8.jpg?t=%E5%A6%82%E6%9E%9C%E6%9C%89%E7%90%86%E6%95%B0a%E3%80%81b%E6%BB%A1%E8%B6%B3%7Cab-2%7C%2B%7C1-b%7C%3D0%2C%E8%AF%95%E6%B1%821+%2Fab%2B1%2Fa%2B1%29%EF%BC%88b%2B1%EF%BC%89%2B1%2F%28a%2B2%29%28b%2B2%29%2B...%2B1%2F%28a%2B2009%29%28b%2B2009%EF%BC%89%E7%9A%84%E5%80%BC)
如果有理数a、b满足|ab-2|+|1-b|=0,试求1 /ab+1/a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2009)(b+2009)的值
如果有理数a、b满足|ab-2|+|1-b|=0,试求1 /ab+1/a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2009)(b+2009)的值
如果有理数a、b满足|ab-2|+|1-b|=0,试求1 /ab+1/a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2009)(b+2009)的值
有理数a、b满足|ab-2|+|1-b|=0
则必有 AB-2=0 1-B=0
===>A=2,B=1
1 /ab+1/a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2009)(b+2009)
=1/(1*2)+1/(2*3)+.+1/(2010*2011)
=1-1/2+1/2-1/3+.+1/2010-1/2011
=1-1/2011=2010/2011
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