1/1*4+1/4*7+1/7*10+1/10*13+...+1/94*97+1/97*100quick!...*99999999999999999999999999999999999999999999999999999999999999...

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/02 21:17:37
1/1*4+1/4*7+1/7*10+1/10*13+...+1/94*97+1/97*100quick!...*99999999999999999999999999999999999999999999999999999999999999...

1/1*4+1/4*7+1/7*10+1/10*13+...+1/94*97+1/97*100quick!...*99999999999999999999999999999999999999999999999999999999999999...
1/1*4+1/4*7+1/7*10+1/10*13+...+1/94*97+1/97*100
quick!...*99999999999999999999999999999999999999999999999999999999999999...

1/1*4+1/4*7+1/7*10+1/10*13+...+1/94*97+1/97*100quick!...*99999999999999999999999999999999999999999999999999999999999999...
1/1*4+1/4*7+1/7*10+1/10*13+...+1/94*97+1/97*100
=1/3(1-1/4)+1/3(1/4-1/7)+1/3(1/7-1/10)+.+1/3(1/97-1/100)
=1/3(1-1/4+1/4-1/7+1/7-1/10+...+1/97-1/100)
=1/3X(1-1/100)
=33/100