计算:1/1*2+1/2*3+1/3*4+...+1/98*99+1/99*1007/2(猜一成语)
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计算:1/1*2+1/2*3+1/3*4+...+1/98*99+1/99*1007/2(猜一成语)
计算:1/1*2+1/2*3+1/3*4+...+1/98*99+1/99*100
7/2(猜一成语)
计算:1/1*2+1/2*3+1/3*4+...+1/98*99+1/99*1007/2(猜一成语)
1、
原式 = (1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) +……+ (1/99 - 1/100)
= 1- 1/100
= 99/100
2、不三不四
记住!
1/n(n+1)=1/n-〔1/(n+1) 〕
1/1*2+1/2*3+1/3*4+...+1/98*99+1/99*100
=1-1/2+1/2-1/3+……+1/99-1/100
=1-1/100
=99/100
7/2
不三不四,即不是3也不是4
1/1*2+1/2*3+1/3*4+...+1/98*99+1/99*100
=(2-1)/1*2+(3-2)/2*3+(4-3)/3*4+...+(100-99)/100*99
=2/1*2-1/1*2+3/2*3-2/2*3+4/3*4-3/3*4+...+100/100*99-99/100*99
=1-1/2+1/2-1/3+1/3-1/4+...+1*99-1/100
=1-1/100
=99/100
不三不四?是吧
百里挑一
原式 =2+3/2+4/3+5/4+...+99/98+100/99
=2+98+(1/2+1/4+4/8+...+1/98)+(1/3+1/5+1/7+...+1/97+1/99)
=2+98+(1-1/98)+(1-1/99)
=102-1/98-1/99