1+1/2+1/3+2/3+1/4+2/4+3/4+...+1/100+2/100+...+99/100.
问题描述:
1+1/2+1/3+2/3+1/4+2/4+3/4+...+1/100+2/100+...+99/100.
答
1+1/2+1/3+2/3+1/4+2/4+3/4+...+1/100+2/100+...+99/100 =1+1/2+(1/3+2/3)+(1/4+2/4+3/4)+(1/5+2/5+3/5+4/5)+……+(1/100+2/100+...+99/100) =1+(0.5+1+1.5+2+2.5+……+49.5) =1+(0.5+49.5)×99/2 =1+2...