若1/2x4+1/4x6+1/6x8+…+1/2n(2n+2)=1001/4008,求n的值

若1/2x4+1/4x6+1/6x8+…+1/2n(2n+2)=1001/4008,求n的值
若1/2x4+1/4x6+1/6x8+…+1/2n(2n+2)=1001/4008,求n的值

若1/2x4+1/4x6+1/6x8+…+1/2n(2n+2)=1001/4008,求n的值
1/n(n+k)=(1/k)(1/n-1/n+k)
1/2x4+1/4x6+1/6x8+…+1/2n(2n+2)=1001/4008
(1/2)(1/2-1/4+1/4-1/6+……+1/2n-1/2n+2)=1001/4008
1/2-1/2n+2=1001/2004
1/2n+2=1/2004
n=1001

提一个1/4出来，原式=1/4(1/1x2+1/2x3+1/3x4+......+1/n(n+1))=1/4(1-1/2+1/2-1/3+1/3-1/4+......+1/n-1/(n+1))=1/4(1-1/(n+1))=n/4(n+1）
所以n=1001