1/2+1/6+1/12+...+1/9702+1/9900(简便运算)简便运算过程要清楚!

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/03 21:05:17
1/2+1/6+1/12+...+1/9702+1/9900(简便运算)简便运算过程要清楚!

1/2+1/6+1/12+...+1/9702+1/9900(简便运算)简便运算过程要清楚!
1/2+1/6+1/12+...+1/9702+1/9900(简便运算)
简便运算过程要清楚!

1/2+1/6+1/12+...+1/9702+1/9900(简便运算)简便运算过程要清楚!
1/2+1/6+1/12+...+1/9702+1/9900
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/98-1/99)+(1/99-1/100)
=1-1/100
=99/100

原式=1*1/2+1/2*1/3+.............+1/99*1/100
=1-1/2+1/2-1/3+....................+1/99-1/100
=1-1/100
=99/100

1/2+1/6+1/12+...+1/9702+1/9900
=1*1/2+1/2*1/3+1/3*1/4+...+1/98*1/99+1/99*1/100
=(1-1/2)+(1/2-1/3)+(1/3_1/4)+...+(1/98-1/99)+(1/99-1/100)
=1-1/100
=99/100

1/2+1/6+1/12+...+1/9702+1/9900=(1-1/2)+(1/2-1/3)+(1/3-1/4)...+(1/99-1/100)=1-1/2+1/2-1/3+1/3-1/4...+1/99-1/100=99/100