求1/x(x+4) + 1/(x+4)(x+8) + 1/(x+8)(x+12) + 1/(x+12)(x+16)的值_数学解答

求1/x(x+4) + 1/(x+4)(x+8) + 1/(x+8)(x+12) + 1/(x+12)(x+16)的值

人气：221 ℃　时间：2020-06-23 11:03:08

解答

1/x(x+4) + 1/(x+4)(x+8) + 1/(x+8)(x+12) + 1/(x+12)(x+16)=(1/4)[1/x-1/(x+4)+1/(x+4)-1/(x+8)+1/(x+8)-1/(x+12)+1/(x+12)-1/(x+16)]=(1/4)[1/x-1/(x+16)]=(1/4)(x+16-x)/[x(x+16)]=4/[x(x+16)]