1/11*13+1/13*15+1/15*17+1/17*19+1/38

1/11*13+1/13*15+1/15*17+1/17*19+1/38
=1/2*(1/11-1/13)+1/2*(1/13-1/15)+1/2*(1/15-1/17)+1/2*(1/17-1/19)+1/2*1/19
=1/2*(1/11-1/13+1/13-1/15+1/15-1/17+1/17-1/19+1/19)
=1/2*1/11
=1/22
【本题用到分数裂项知识:1/［n*(n+2)］=1/2*［1/n-1/(n+2)］】