化简1/(2*5)+1/(5*8)+1/(8*11)+…+1/[（3n-1）*（3n+2）]=
问题描述：
化简1/(2*5)+1/(5*8)+1/(8*11)+…+1/[（3n-1）*（3n+2）]=
答
1/[（3n-1）*（3n+2）]=1/3*{1/(3n-1)-1/(3n+2)}
原式＝1/3*{1/2-1/5+1/5-1/8+1/8-1/11+...+1/(3n-1)-1/(3n+2)}
=1/3*{1/2-1/(3n+2)}
=n/(6n+4)