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比较难的解方程!解方程1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+~+1/(x+2005)(x+2006)==1/(2x+4012)
题目详情
比较难的解方程!
解方程
1/(x+1)(x+2) + 1/(x+2)(x+3) + 1/(x+3)(x+4)+~+ 1/(x+2005)(x+2006) =
= 1/(2x+4012)
解方程
1/(x+1)(x+2) + 1/(x+2)(x+3) + 1/(x+3)(x+4)+~+ 1/(x+2005)(x+2006) =
= 1/(2x+4012)
▼优质解答
答案和解析
因为1/(x+1)(x+2)=1/(x+1)-1/(x+2)
所以 方程左边=1/(x+1)-1/(x+2)+ 1/(x+2)-1/(x+3)+…+ 1/(x+2005)-1/(x+2006)=1/(x+1)-1/(x+2006)= 1/(2x+4012)=1/2(x+2006)
1/(x+1)=3/2(x+2006)
(2x+4012)=3x+3
x=4009
所以 方程左边=1/(x+1)-1/(x+2)+ 1/(x+2)-1/(x+3)+…+ 1/(x+2005)-1/(x+2006)=1/(x+1)-1/(x+2006)= 1/(2x+4012)=1/2(x+2006)
1/(x+1)=3/2(x+2006)
(2x+4012)=3x+3
x=4009
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