观察下列各式1/2=1/1x2=1/1-1/21/6=1/2x3=1/2-1/31/12=1/3x4=1/3-1/41/20=1/4x5=1/4-1/51/30=1/5x6=1/5-1/6.请你猜想出(1)中的特点的一般规律,用含X(X表示整数)的等式表示出来请利用上述规律计算(有过程)1/2+1/6+1/12.+1/
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![观察下列各式1/2=1/1x2=1/1-1/21/6=1/2x3=1/2-1/31/12=1/3x4=1/3-1/41/20=1/4x5=1/4-1/51/30=1/5x6=1/5-1/6.请你猜想出(1)中的特点的一般规律,用含X(X表示整数)的等式表示出来请利用上述规律计算(有过程)1/2+1/6+1/12.+1/](/uploads/image/z/2656496-56-6.jpg?t=%E8%A7%82%E5%AF%9F%E4%B8%8B%E5%88%97%E5%90%84%E5%BC%8F1%2F2%3D1%2F1x2%3D1%2F1-1%2F21%2F6%3D1%2F2x3%3D1%2F2-1%2F31%2F12%3D1%2F3x4%3D1%2F3-1%2F41%2F20%3D1%2F4x5%3D1%2F4-1%2F51%2F30%3D1%2F5x6%3D1%2F5-1%2F6.%E8%AF%B7%E4%BD%A0%E7%8C%9C%E6%83%B3%E5%87%BA%281%29%E4%B8%AD%E7%9A%84%E7%89%B9%E7%82%B9%E7%9A%84%E4%B8%80%E8%88%AC%E8%A7%84%E5%BE%8B%2C%E7%94%A8%E5%90%ABX%28X%E8%A1%A8%E7%A4%BA%E6%95%B4%E6%95%B0%29%E7%9A%84%E7%AD%89%E5%BC%8F%E8%A1%A8%E7%A4%BA%E5%87%BA%E6%9D%A5%E8%AF%B7%E5%88%A9%E7%94%A8%E4%B8%8A%E8%BF%B0%E8%A7%84%E5%BE%8B%E8%AE%A1%E7%AE%97%28%E6%9C%89%E8%BF%87%E7%A8%8B%291%2F2%2B1%2F6%2B1%2F12.%2B1%2F)
观察下列各式1/2=1/1x2=1/1-1/21/6=1/2x3=1/2-1/31/12=1/3x4=1/3-1/41/20=1/4x5=1/4-1/51/30=1/5x6=1/5-1/6.请你猜想出(1)中的特点的一般规律,用含X(X表示整数)的等式表示出来请利用上述规律计算(有过程)1/2+1/6+1/12.+1/
观察下列各式
1/2=1/1x2=1/1-1/2
1/6=1/2x3=1/2-1/3
1/12=1/3x4=1/3-1/4
1/20=1/4x5=1/4-1/5
1/30=1/5x6=1/5-1/6
.
请你猜想出(1)中的特点的一般规律,用含X(X表示整数)的等式表示出来
请利用上述规律计算(有过程)
1/2+1/6+1/12.+1/(n-1)n+1/n(n+1)
请利用上述规律,解方程
1/(x-4)(x-3)+1/(x-3)(x-2)+1/(x-2)(x-1)+1/(x-1)x+1/x(x+1)=1/x+1
原方程可以变形如下:
观察下列各式1/2=1/1x2=1/1-1/21/6=1/2x3=1/2-1/31/12=1/3x4=1/3-1/41/20=1/4x5=1/4-1/51/30=1/5x6=1/5-1/6.请你猜想出(1)中的特点的一般规律,用含X(X表示整数)的等式表示出来请利用上述规律计算(有过程)1/2+1/6+1/12.+1/
1/2+1/6+1/12.+1/(n-1)n+1/n(n+1)
=1/1*2+1/2*3+1/3*4+...+1/(n-1)n+1/n(n+1)
=1-1/2+1/2-1/3+1/3-1/4+...+1/(n-1)-1/n+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)
1/(x-4)(x-3)+1/(x-3)(x-2)+1/(x-2)(x-1)+1/(x-1)x+1/x(x+1)=1/x+1
1/(x-4)-1/(x-3)+1/(x-3)-1/(x-2)+1/(x-2)-1/(x-1)+1/(x-1)-1/x+1/x-1/(x+1)=1/(x+1)
1/(x-4)-1/(x+1)=1/(x+1)
1/(x-4)=2/(x+1)
2x-8=x+1
x=9
1/X - 1/(X+1) = 1/ ( X(X+1) )
1/2+1/6+1/12......+1/(n-1)n+1/n(n+1)
= 1/1-1/2+1/2-1/3+1/3-1/4+.....+1/n-1/(n+1)
= n/(n+1).
利用上述规律,解方程
1/(x-4)(x-3)+1/(x-3)(x-2)+1/(x-2)(x-1)+1/(x-1)x+1/x(x+1)=1/x+1
原方程可以变形如下: 1/(x-4)-1/(x+1) = 1/(x+1)
(x+1) = 2x-8
x = 9
1/(x-1)x=1/(x-1)-1/x
1/2+1/6+1/12......+1/(n-1)n+1/n(n+1)
=1/1-1/2+1/2-1/3+1/3-1/4+...+1/n-1/(n+1)
=1-1/(n+1)
1/(x-4)(x-3)+1/(x-3)(x-2)+1/(x-2)(x-1)+1/(x-1)x+1/x(x+1)
=1/(x-4)-1/(x-3)+1/(x-3)-1/(x-2)+..+1/x-1/(x+1)
=1/(x-4)-1/(x+1)=1/x+1
1/(x*(x+1))=1/x-1/(x+1);
An=1/n-1/(1+n);
和=1/1-1/2+1/2-1/3+1/3-1/4……1/(n-1)-1/n+1/n-1/(n+1)=1-1/(n+1);
原方程可化简为:1/(x-4)-1/(x+1)=1/x+1