已知1/1×2=1-1/2,1/2×3=1/2-1/3,1/3×4=1/3-1/4.,则1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)
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![已知1/1×2=1-1/2,1/2×3=1/2-1/3,1/3×4=1/3-1/4.,则1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)](/uploads/image/z/3907387-19-7.jpg?t=%E5%B7%B2%E7%9F%A51%2F1%C3%972%3D1-1%2F2%2C1%2F2%C3%973%3D1%2F2-1%2F3%2C1%2F3%C3%974%3D1%2F3-1%2F4.%2C%E5%88%991%2Fx%28x%2B1%29%2B1%2F%28x%2B1%29%28x%2B2%29%2B1%2F%28x%2B2%29%28x%2B3%29)
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已知1/1×2=1-1/2,1/2×3=1/2-1/3,1/3×4=1/3-1/4.,则1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)
已知1/1×2=1-1/2,1/2×3=1/2-1/3,1/3×4=1/3-1/4.,则1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)
已知1/1×2=1-1/2,1/2×3=1/2-1/3,1/3×4=1/3-1/4.,则1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)
=1/x-1/(x+3)
原式=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)
=1/x-1/(x+3)
=3/<(x+3)*x>
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)=1/x-1/(x+3)=3/[x(x+3)]
此题就是利用拆项达到把中间项相互抵消消项的目的,1/n*m=(1/n-1/m)/(m-n),m>n