1/1*2+1/2*3+1/3*4+L;+1/n（n+1）= 1/2*4+1/4*6+1/6*8+L+1/2006*2008=_数学解答

1/1*2+1/2*3+1/3*4+L;+1/n（n+1）= 1/2*4+1/4*6+1/6*8+L+1/2006*2008=

人气：411 ℃　时间：2020-06-27 22:03:29

解答

1/1*2+1/2*3+1/3*4+L;+1/n（n+1）= 1-1/2+1/2-1/3+1/3.+1/n-1/(n+1)=1-1/(n+1)1/2*4+1/4*6+1/6*8+L+1/2006*2008=1/2(1/1*2+1/2*3+1/3*4.+1/1003-1/1004)=1/2(1-1/2+1/2-1/3+1/3...-1/1004)=1/2(1-1/2004)=1/2*2003/2...