已知1/1x2=1-1/2;1/2x3=1/2-1/3,1/3x4=1/3-1/4,1/4x5=1/4-1/5;…1/(n-1)n=1/n-1-1/n请你根据上式中包含的规律,求不等式x/2+x/6+(1/12)x+(1/20)x+…+x/(n-1)n>n-1的解集.
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![已知1/1x2=1-1/2;1/2x3=1/2-1/3,1/3x4=1/3-1/4,1/4x5=1/4-1/5;…1/(n-1)n=1/n-1-1/n请你根据上式中包含的规律,求不等式x/2+x/6+(1/12)x+(1/20)x+…+x/(n-1)n>n-1的解集.](/uploads/image/z/2593831-31-1.jpg?t=%E5%B7%B2%E7%9F%A51%2F1x2%3D1-1%2F2%3B1%2F2x3%3D1%2F2-1%2F3%2C1%2F3x4%3D1%2F3-1%2F4%2C1%2F4x5%3D1%2F4-1%2F5%3B%E2%80%A61%2F%EF%BC%88n-1%EF%BC%89n%3D1%2Fn-1-1%2Fn%E8%AF%B7%E4%BD%A0%E6%A0%B9%E6%8D%AE%E4%B8%8A%E5%BC%8F%E4%B8%AD%E5%8C%85%E5%90%AB%E7%9A%84%E8%A7%84%E5%BE%8B%2C%E6%B1%82%E4%B8%8D%E7%AD%89%E5%BC%8Fx%2F2%2Bx%2F6%2B%EF%BC%881%2F12%EF%BC%89x%2B%EF%BC%881%2F20%EF%BC%89x%2B%E2%80%A6%2Bx%2F%EF%BC%88n-1%EF%BC%89n%EF%BC%9En-1%E7%9A%84%E8%A7%A3%E9%9B%86.)
已知1/1x2=1-1/2;1/2x3=1/2-1/3,1/3x4=1/3-1/4,1/4x5=1/4-1/5;…1/(n-1)n=1/n-1-1/n请你根据上式中包含的规律,求不等式x/2+x/6+(1/12)x+(1/20)x+…+x/(n-1)n>n-1的解集.
已知1/1x2=1-1/2;1/2x3=1/2-1/3,1/3x4=1/3-1/4,1/4x5=1/4-1/5;…1/(n-1)n=1/n-1-1/n
请你根据上式中包含的规律,求不等式x/2+x/6+(1/12)x+(1/20)x+…+x/(n-1)n>n-1的解集.
已知1/1x2=1-1/2;1/2x3=1/2-1/3,1/3x4=1/3-1/4,1/4x5=1/4-1/5;…1/(n-1)n=1/n-1-1/n请你根据上式中包含的规律,求不等式x/2+x/6+(1/12)x+(1/20)x+…+x/(n-1)n>n-1的解集.
x/2+x/6+(1/12)x+(1/20)x+…+x/(n-1)n
= x ( 1/2 + 1/(2*3) + 1/(3*4) + 1/(4*5) + ... + 1/(n-1)n )
= x (1/2 + 1/2-1/3 + 1/3-1/4 + 1/4-1/5 + ...+ 1/(n-1) - 1/n)
= x (1/2 +1/2 -1/n)
= x(n-1)/n
所以原不等式即 x(n-1)/n > n-1
因为 n-1 > 0,所以
x > n
即x[1-1/2+1/2-1/3+……+1/(n-1)-1/n]>n-1
x(1-1/n)>n-1
x(n-1)/n>n-1
显然这里n-1>0
n>1
所以x>n