1/1*3*5+1/3*5*7+1/5*7*9+1/7*9*11+1/9*11*15+1/11*13*15=

1/1*3*5+1/3*5*7+1/5*7*9+1/7*9*11+1/9*11*15+1/11*13*15

=1/4(1/1*3-1/3*5)+1/4(1/3*5-1/5*7)+...+1/4(1/11*13-1/13*15)

=1/4(1/1*3-1/3*5+1/3*5-1/5*7+.....+1/11*13-1/13*15)

=1/4(1/1*3-1/13*15)

=1/4(1/3-1/195)

=1/4*64/195

=16/195

1/n(n+2)(n+4)=1/4*(n+4-n)/n(n+2)(n+4)
=1/4*[1/n(n+2)－1/(n+2)(n+4)]
所以原式=1/4[1/1*3－1/3*5+1/3*5－1/5*7
+1/5*7－1/7*9+1/7*9－1/9*11
+1/9*11－1/11*13 +1/11*13－1/13*15]
=1/4[1/1*3－1/13*15]
=1/4*[65/195－1/195]
=16/195