已知n系正整数,an=1*2*3*4*.n,则a1/a3+a2/a4+a2010/a2012+a2011/2013=

an=1×2×...×n
a(n+2)+1×2×...×n×(n+1)×(n+2)
an/a(n+2)=(1×2×...×n)/[1×2×...×(n+2)]=1/[(n+1)(n+2)]=1/(n+1) -1/(n+2)
a1/a3+a2/a4+...+a2010/2012+a2011/2013
=1/2 -1/3+1/3-1/4+...+1/2011-1/2012+1/2012-1/2013
=1/2 -1/2013
=2011/4026