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小学数学奥数六年级1/1*2*3+1/2*3*4+1/3*4*5+...1/98*99*100

=1/2*(1/1*2-1/2*3)+1/2*(1/2*3-1/3*4)+……+1/2*(1/98*99-1/99*100)=1/2*(1/1*2-1/2*3+1/2*3-1/3*4+……+1/98*99-1/99*100)=1/2*(1/1*2-1/99*100)=4949/19800

方法1:公式:y=1/n(n+1) n=1、299 y=1/n-1/(n+1) =1-1/2+1/2-1/3+1/3-1/41/99-1/100 =1-1/100 =99/100方法2:1/1*2+1/2*3=2/3 1/1*2+1/2*3+1/3*4=3/4 1/1*2+1/2*3+1/3*4+1/4*5=4/5 1/1*2+1/2*3+1/3*4+1/4*5+1/99*100=99/100

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/39*40=1-1/2+1/2-1/3++1/39-1/40=1-1/40=39/40

1^3+2^3+3^3++(n-1)^3+n^3=1/4*n^2*(n+1)^2

1/n*1/(n+1)=1/n-1/(n+1) 这个式子=1-1/10=9/10

1/1*2+1/2*3+1/3*4++1/29*30=1-1/2+1/2-1/3+1/3+1/29-1/30=1-1/30=29/30 请采纳

1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+……+1/(98*99)+1/(99*100) =1-1/2+1/2-1/3+.+1/99-1/100=1-1/100=99/100

原式=1-1/2+1/2-1/3+1/3-1/4+1/99-1/100=1-1/100=99/100

答案:99/100解题方法:=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)++(1/99-1/100) =1-1/100 =99/100

原式=1/2*[2/(1*2*3)+2/(2*3*4)++2/(98*99*100)] =1/2*[(3-1)/(1*2*3)+(4-2)/(2*3*4)++(100-98)/(98*99*100)] =1/2*[3/(1*2*3)-1/(1*2*3)+4/(2*3*4)-2/(2*3*4)++100/(98*99*100)-98/(98*99*100)] =1/2*[1/(1*2)-1/(2*3)+1/(2*3)-1/(3*4)++1/(98*99)-1/(99*100)] =1/2*[1/2-1/9900] =4949/19800

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