已知:字母a、b满足√(a-1)+√(b-2)=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2009)(b+2009)
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![已知:字母a、b满足√(a-1)+√(b-2)=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2009)(b+2009)](/uploads/image/z/8708967-63-7.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BC%9A%E5%AD%97%E6%AF%8Da%E3%80%81b%E6%BB%A1%E8%B6%B3%E2%88%9A%EF%BC%88a-1%29%2B%E2%88%9A%28b-2%29%3D0%2C%E6%B1%821%EF%BC%8Fab%2B1%2F%28a%2B1%29%28b%2B1%29%2B1%2F%28a%2B2%29%28b%2B2%29%2B%E2%80%A6%E2%80%A6%2B1%2F%28a%2B2009%29%28b%2B2009%29)
已知:字母a、b满足√(a-1)+√(b-2)=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2009)(b+2009)
已知:字母a、b满足√(a-1)+√(b-2)=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2009)(b+2009)
已知:字母a、b满足√(a-1)+√(b-2)=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2009)(b+2009)
√(a-1)+√(b-2)=0
a-1=b-2=0
a=1b=2
原式=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
2011\2012
无解
a-1=0,b-2=0
a=1,b=2
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
a=1
b=2
1/1x2+1/2x3+1/3x4+1/4x5+········+1/2009x2010+1/2010x2011
=1-1/2+1/2-1/3+1/3-1/4+···········+1/2009-1/2010+1/2010-1/2011
=1-1/2011
=2010/2011
给不给分啊~~~~~!!!!
饿得不行了1-1...
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a=1
b=2
1/1x2+1/2x3+1/3x4+1/4x5+········+1/2009x2010+1/2010x2011
=1-1/2+1/2-1/3+1/3-1/4+···········+1/2009-1/2010+1/2010-1/2011
=1-1/2011
=2010/2011
给不给分啊~~~~~!!!!
饿得不行了
收起
由题的a=1,b=2 所以b=a+1
1/(a+n)-1/(b+n)=【b+n-(a+n)】/(a+n)(b+n)=(b-a)/(a+n)(b+n)=1/(a+n)(b+n)
所以
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2009)(b+2009)
=1/ab+1/(a+1)-1/(b+1)+1/(a+2)-1/(b+2)+.....
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由题的a=1,b=2 所以b=a+1
1/(a+n)-1/(b+n)=【b+n-(a+n)】/(a+n)(b+n)=(b-a)/(a+n)(b+n)=1/(a+n)(b+n)
所以
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2009)(b+2009)
=1/ab+1/(a+1)-1/(b+1)+1/(a+2)-1/(b+2)+......+1/(a+2009)-1/(b+2009)
=1/2+1/2-1/3+1/3-1/4+.....+1/2010-1/2011
=1-1/2011
=2010/2011
收起