5x8分之1+8x11分之一+11x14分之一+14x17分之一+.+2009x2012分之一.最好有口述,谢

1/n-1/(n+3)=(n+3)/n(n+3)-n/n(n+3)=3/n(n+3),故1/n（n+3）=[1/n-1/(n+3)]/3
则原式=(1/5-1/8)/3+(1/8-1/11)/3+……(1/2009-1/2012)/3
=(1/5-1/8+1/8-1/11……+1/2009-1/2012)/3
=(1/5-1/2012)/3
=2017/30180