已知;|ab-2|与|b-1|互为相反数.试求代数式1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2009)(b+2009)
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![已知;|ab-2|与|b-1|互为相反数.试求代数式1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2009)(b+2009)](/uploads/image/z/3035783-47-3.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BC%9B%7Cab-2%7C%E4%B8%8E%7Cb-1%7C%E4%BA%92%E4%B8%BA%E7%9B%B8%E5%8F%8D%E6%95%B0.%E8%AF%95%E6%B1%82%E4%BB%A3%E6%95%B0%E5%BC%8F1%2Fab%2B1%2F%28a%2B1%29%28b%2B1%29%2B1%2F%28a%2B2%29%28b%2B2%29%2B...%2B1%2F%28a%2B2009%29%28b%2B2009%29)
已知;|ab-2|与|b-1|互为相反数.试求代数式1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2009)(b+2009)
已知;|ab-2|与|b-1|互为相反数.试求代数式1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2009)(b+2009)
已知;|ab-2|与|b-1|互为相反数.试求代数式1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2009)(b+2009)
|ab-2|与|b-1|互为相反数.
所以ab-2=0,b-1=0
a=2,b=1
原式=1/(1x2)+1/(2x3)+1/(3x4)+...+1/(2010x2011)
=1-1/2+1/2-1/3+1/3-1/4+...+1/2010-1/2011
=1-1/2011
=2010/2011
|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+2009)(b+2009)
=1/2x1+1/3x2+...+1/2011x2010
=1-1/2+1/2-1/3+...+1/2010-1/2011
=1-1/2011
=2010/2011
|ab-2|与|b-1|互为相反数说明|ab-2|=0 |b-1|=0
ab=2 b=1 a=2
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2009)(b+2009)
=1/2+1/2×3+1/3×4+.....+1/2010×2011
=1-1/2+1/2-1/3+1/3-1/4+....+1/2010-1/2011
=1-1/2011
=2010/2011