简算:1/1*4+1/4*7+1/7*10+...+1/100*103要详细有悬赏快,紧急!
问题描述：
简算:1/1*4+1/4*7+1/7*10+...+1/100*103
要详细
有悬赏
快,紧急!
答
1/1×4+1/4×7+1/7×10+...+1/100×103
=(1/3)×(3/1×4+3/4×7+3/7×10+...+3/100×103)
=(1/3)×[(1-1/4)+(1/4-1/7)+(1/7-1/10)+...+(1/100-1/103)]
=(1/3)×(1-1/4+1/4-1/7+1/7-1/10+...+1/100-1/103)
=(1/3)×(1-1/103)
=(1/3)×(102/103)
=34/103
答
1/4=(1-1/4)/3,1/4*7=(1/4-1/7)/3
1/1*4+1/4*7+1/7*10+...+1/100*103
=[(1-1/4)+(1/4-1/7)+……+(1/100-1/103)]/3
=(1-1/103)/3
=34/103
答
1/100*103=1/3[(1/100)-(1/103)]
代入,1/1*4+1/4*7+1/7*10+...+1/100*103
=1/3(1-1/4+1/4-1/7+……+1/100-1/103）
=1/3*(1-1/103)
=34/103