数学问题!!!急!!!在线等!!!
请用简便方法计算:1/(2*5)+1/(5*8)+1/(8*11)+1/(11*14)+1/(14*17)+1/(17*20)=?注:题目中"/"都代表分数线!要用简便方法!!!
参考答案:原式=1/3*(1/2-1/5+1/5-1/8+1/8-……-1/20)=3/20
原理:
1/(n*m)=1/(m-n)*(1/n-1/m)
请用简便方法计算:1/(2*5)+1/(5*8)+1/(8*11)+1/(11*14)+1/(14*17)+1/(17*20)=?注:题目中"/"都代表分数线!要用简便方法!!!
参考答案:原式=1/3*(1/2-1/5+1/5-1/8+1/8-……-1/20)=3/20
原理:
1/(n*m)=1/(m-n)*(1/n-1/m)