作业帮数学题The mathematics is inscribed
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数学题The mathematics is inscribed
已知丨ab-2丨与丨b-1丨互为相反数,试求代数式1/ab+1/（a+1）（b+1）+1/（a+2）（b+2）+……1/（a+2008）（b+2009）的值.
已知丨ab-2丨与丨b-1丨互为相反数,试求代数式1/ab+1/（a+1）（b+1）+1/（a+2）（b+2）+……1/（a+2008）（b+2009）的值.
丨ab-2丨与丨b-1丨互为相反数
即丨ab-2丨+丨b-1丨=0
绝对值大于等于0
相加为0则各项均为0
所以ab-2=0
b-1=0
所以b=1,a=2
1/ab+1/（a+1）（b+1）+1/（a+2）（b+2）+……1/（a+2008）（b+2009）
=1/1*2+1/2*3+1/3*4+……+1/2009*2010
=1-1/2+1/2-1/3+1/3-1/4……+1/2009-1/2010
中间抵消
=1-1/2010
=2009/2010
是挺难的,两道题目结合在一起啊
即丨ab-2丨+丨b-1丨=0
绝对值大于等于0
相加为0则各项均为0
所以ab-2=0
b-1=0
所以b=1,a=2
1/ab+1/（a+1）（b+1）+1/（a+2）（b+2）+……1/（a+2008）（b+2009）
=1/1*2+1/2*3+1/3*4+……+1/2009*2010
=1-1/2+1/2-1/3+1/3-1/4……+1/2009-1/2010
中间抵消
=1-1/2010
=2009/2010
是挺难的,两道题目结合在一起啊
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