已知ab是有理数,且满足(a-1)²+丨b-2丨=0,求ab分之1+ (a+1)(b+1)分之1+(a+2)(b+2)分之1+····+(a+2013)(b+2013)分之1的值.
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![已知ab是有理数,且满足(a-1)²+丨b-2丨=0,求ab分之1+ (a+1)(b+1)分之1+(a+2)(b+2)分之1+····+(a+2013)(b+2013)分之1的值.](/uploads/image/z/1124894-38-4.jpg?t=%E5%B7%B2%E7%9F%A5ab%E6%98%AF%E6%9C%89%E7%90%86%E6%95%B0%2C%E4%B8%94%E6%BB%A1%E8%B6%B3%EF%BC%88a-1%29%26%23178%3B%2B%E4%B8%A8b-2%E4%B8%A8%3D0%2C%E6%B1%82ab%E5%88%86%E4%B9%8B1%2B+%EF%BC%88a%2B1%29%28b%2B1%29%E5%88%86%E4%B9%8B1%2B%EF%BC%88a%2B2%29%28b%2B2%29%E5%88%86%E4%B9%8B1%2B%C2%B7%C2%B7%C2%B7%C2%B7%2B%EF%BC%88a%2B2013%29%28b%2B2013%29%E5%88%86%E4%B9%8B1%E7%9A%84%E5%80%BC.)
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已知ab是有理数,且满足(a-1)²+丨b-2丨=0,求ab分之1+ (a+1)(b+1)分之1+(a+2)(b+2)分之1+····+(a+2013)(b+2013)分之1的值.
已知ab是有理数,且满足(a-1)²+丨b-2丨=0,求ab分之1+ (a+1)(b+1)分之1+(a+2)(b+2)分之1+····+(a+2013)(b+2013)分之1的值.
已知ab是有理数,且满足(a-1)²+丨b-2丨=0,求ab分之1+ (a+1)(b+1)分之1+(a+2)(b+2)分之1+····+(a+2013)(b+2013)分之1的值.
(a-1)²+丨b-2丨=0
所以a-1=0,b-2=0
a=1,b=2
所以原式=1/1×2+1/2×3+……+1/2014×2015
=1-1/2+1/2-1/3+……+1/2014-1/2015
=1-1/2015
=2014/2015