一道初一找规律的数学题,下面是题,我主要要的是讲解啊!a=2,b=11/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+·····(a+2005)(b+2005)的值
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![一道初一找规律的数学题,下面是题,我主要要的是讲解啊!a=2,b=11/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+·····(a+2005)(b+2005)的值](/uploads/image/z/4670877-21-7.jpg?t=%E4%B8%80%E9%81%93%E5%88%9D%E4%B8%80%E6%89%BE%E8%A7%84%E5%BE%8B%E7%9A%84%E6%95%B0%E5%AD%A6%E9%A2%98%2C%E4%B8%8B%E9%9D%A2%E6%98%AF%E9%A2%98%2C%E6%88%91%E4%B8%BB%E8%A6%81%E8%A6%81%E7%9A%84%E6%98%AF%E8%AE%B2%E8%A7%A3%E5%95%8A%21a%3D2%2Cb%3D11%2Fab%2B1%2F%EF%BC%88a%2B1%29%28b%2B1%29%2B1%2F%EF%BC%88a%2B2%29%28b%2B2%29%2B%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%28a%2B2005%29%28b%2B2005%EF%BC%89%E7%9A%84%E5%80%BC)
一道初一找规律的数学题,下面是题,我主要要的是讲解啊!a=2,b=11/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+·····(a+2005)(b+2005)的值
一道初一找规律的数学题,下面是题,我主要要的是讲解啊!
a=2,b=1
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+·····(a+2005)(b+2005)的值
一道初一找规律的数学题,下面是题,我主要要的是讲解啊!a=2,b=11/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+·····(a+2005)(b+2005)的值
1/ab = 1/(2*1)=1/1-1/2
1/(a+1)(b+1)=1/(3*2)=1/2-1/3
1/(a+2)(b+2)=1/(4*3)=1/3-1/4
……………………
1/(a+2004)(b+2004)=1/2005-1/2006
1/(a+2005)(b+2005)=1/2006-1/2007
以上各式相加得
1-1/2+1/2-1/3+1/3-1/4…………+1/2005-1/2006+1/2006-1/2007
=1-1/2007
=2006/2007
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+·····(a+2005)(b+2005)
=1/2*1+1/3*2+1/4*3+……1/2007*2006
=1-1/2+1/2-1/3+1/3-1/4+……1/2006-1/2007
=1-1/2007
=2006/2007
解法如下:
1/(a+2004)(b+2004)=1/2005-1/2006
1/(a+2005)(b+2005)=1/2006-1/2007
以上各式相加得
1-1/2+1/2-1/3+1/3-1/4…………+1/2005-1/2006+1/2006-1/2007
=1-1/2007
=2006/2007
希望能帮到你
因为a=2,b=1
所以1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+•……+1/(a+2005)(b+2005)
=1/(2×1)+1/(3×2)+1/(4×3)+……+1/(2007×2006)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2006-1/2007)
=1+(-1/2+1/2)+(-1/3+1/3)+(-1/4+1/4)……+(-1/2006+1/2006)-1/2007
=1-1/2007=2006/2007