分类：教育/科学-学习帮助
问题：高二数列题求和问题求Sn=1/(1*4)+1/(4*7)+1/( 
求Sn=1/(1*4)+1/(4*7)+1/(7*10)+......+1/(3n-2)(3n+1)
要求详细解答，谢谢
回答：认真分析Sn=1/(1*4)+1/(4*7)+1/(7*10)+......+1/(3n-2)(3n+1)
就会发现：1/(1*4)＝1/3 *(1/1 -  1/4)
        　1/(4*7)＝1/3 *(1/4 -  1/7)
......
   1/(3n-2)(3n+1)＝1/3 *[1/(3n-2)-  1/(3n+1)]

所以Sn=1/(1*4)+1/(4*7)+1/(7*10)+......+1/(3n-2)(3n+1)
　　　即Sn＝1/3 [1/1 - 1/4 + 1/4 - 1/7 +...... 1/(3n-2)- 1/(3n+1)] 
      即Sn＝1/3 [1/1 -  1/(3n+1)] 
      即Sn＝1/3 [1 - 1/(3n+1)] 
      即Sn＝n/(3n+1) 

我想，应该不会错吧