简便运算1/(2*5)+1/(3*5)+1/(8*11)+……+1/(20*23)=

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/25 00:51:57
简便运算1/(2*5)+1/(3*5)+1/(8*11)+……+1/(20*23)=简便运算1/(2*5)+1/(3*5)+1/(8*11)+……+1/(20*23)=简便运算1/(2*5)+1/(3

简便运算1/(2*5)+1/(3*5)+1/(8*11)+……+1/(20*23)=
简便运算1/(2*5)+1/(3*5)+1/(8*11)+……+1/(20*23)=

简便运算1/(2*5)+1/(3*5)+1/(8*11)+……+1/(20*23)=
是不是题目出错了
如果是把“1/(3*5)+”换成“1/(5*8)+”就对了
2,5,8,11,14,17,20,23..顺序增加3
1/(2*5)+1/(5*8)+1/(8*11)+...+1/(20*23)
=(1/3)*(1/2-1/5+1/5-1/8+1/8-1/11+.+1/20-1/23)
=(1/3)*(1/2-1/23)
=7/46

1/2-1/5=3/(2*5)
1/5-1/8=3/(5*8)...
1/(2*5)+1/(3*5)+1/(8*11)+……+1/(20*23)
=1/3*(1/2-1/5+1/5-1/8+....+1/20-1/23)
=1/3*(1/2-1/23)
=1/3*21/46
=7/46