如果有理数a,b 满足a等于2,b等于1,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2004)(b+2004)的值
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![如果有理数a,b 满足a等于2,b等于1,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2004)(b+2004)的值](/uploads/image/z/165293-53-3.jpg?t=%E5%A6%82%E6%9E%9C%E6%9C%89%E7%90%86%E6%95%B0a%2Cb+%E6%BB%A1%E8%B6%B3a%E7%AD%89%E4%BA%8E2%2Cb%E7%AD%89%E4%BA%8E1%2C%E6%B1%821%EF%BC%8Fab%2B1%2F%28a%2B1%29%28b%2B1%29%2B1%EF%BC%8F%28a%2B2%29%28b%2B2%29%2B%E2%80%A6%2B1%EF%BC%8F%28a%2B2004%29%28b%2B2004%29%E7%9A%84%E5%80%BC)
如果有理数a,b 满足a等于2,b等于1,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2004)(b+2004)的值
如果有理数a,b 满足a等于2,b等于1,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2004)(b+2004)的值
如果有理数a,b 满足a等于2,b等于1,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2004)(b+2004)的值
a等于2,b等于1代人
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2004)(b+2004)
=1/1*2+1/2*3+1/3*4+…+1/2005*2006
=1-1/2+1/2-1/3+1/3-1/4+…+1/2005-1/2006
=1-1/2006=2005/2006
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2004)(b+2004)
=(1/b-1/a).1/(a-b)+(1/(b+1)-1/(a+1).1/(a-b)+.....+)+(1/(b+2004)-1/(a+2004).1/(a-b)
=(1/b+1/(b+1)+...+1/(b+2004)-(1/a+1/(a+1)+...+1/(a+2004)<...
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1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2004)(b+2004)
=(1/b-1/a).1/(a-b)+(1/(b+1)-1/(a+1).1/(a-b)+.....+)+(1/(b+2004)-1/(a+2004).1/(a-b)
=(1/b+1/(b+1)+...+1/(b+2004)-(1/a+1/(a+1)+...+1/(a+2004)
=(1+1/2+1/3+...+1/2005)-(1/2+1/3+...+1/2006)
=2005/2006 我是数学百事通,数学问题想不通,就上数学百事通
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