作业帮化简1/(2*5)+1/(5*8)+1/(8*11)+…+1/[（3n-1）*（3n+2）]=
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/29 21:02:05
![化简1/(2*5)+1/(5*8)+1/(8*11)+…+1/[（3n-1）*（3n+2）]=](/uploads/image/z/2181098-2-8.jpg?t=%E5%8C%96%E7%AE%801%2F%282%2A5%29%2B1%2F%285%2A8%29%2B1%2F%288%2A11%29%2B%E2%80%A6%2B1%2F%5B%EF%BC%883n-1%EF%BC%89%2A%EF%BC%883n%2B2%EF%BC%89%5D%3D)
化简1/(2*5)+1/(5*8)+1/(8*11)+…+1/[（3n-1）*（3n+2）]=
化简1/(2*5)+1/(5*8)+1/(8*11)+…+1/[（3n-1）*（3n+2）]=
化简1/(2*5)+1/(5*8)+1/(8*11)+…+1/[（3n-1）*（3n+2）]=
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)
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