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2x3/1+3x4/1+4x5/1+.....99x100/1

1/(2*3) + 1/(3*4) + 1/(4*5) + + 1/(99*100)= (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + + (1/99 - 1/100)= 1/2 +(1/3 - 1/3) + (1/4 - 1/4) + + (1/99 - 1/99) - 1/100= 1/2 - 1/100= 0.49

1/1*2=1-1/2 1/2*3=1/2-1/3 1x2\1+2x3\1+3x4\1+4x5\1++99x100\1 =1-1/2+1/2-1/3+1/3-+1/99-1/100 =1-1/100 =99/100 =0.99

1/2+1/2x3+1/3x4+1/4x5++1/99x100=1/1*2+1/2x3+1/3x4+1/4x5++1/99x100=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/99-1/100=1-1/100=99/100

你问的第一个题用裂项法 原式=1-1/2+1/2-1/3+1/3-1/4+-1/99+1/100=100/101

因为 1/1*2 = 1 - 1/2 1/2*3 = 1/2 - 1/3 依此类推 1/99*100 = 1/99 - 1/100 所以 原式 = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + + 1/99 - 1/00 = 1 - 1/100 = 99/100

1x2+2x3+3x4+4x5..99x100=1/3*1*2*3+1/3*[2*3*4-1*2*3]+1/3[3*4*5-2*3*4]++1/3[99*100*101-98*99*100]=1/3[1*2*3+2*3*4-1*2*3+3*4*5-2*3*4+.+99*100*101-98*99*100]=1/3*99*100*101=3300*101=333300公式:sn=1*2+2*3+3*4++n(n+1)=n(n+1)(n+2)/3

1/1*2=1-1/21/2*3=1/2-1/31x2\1+2x3\1+3x4\1+4x5\1++99x100\1=1-1/2+1/2-1/3+1/3-+1/99-1/100=1-1/100=99/100=0.99

=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5******+1/98-1/99+1/99-1/100 =1-1/100 =99/100

1/2+1/2x3+1/3x4+1/4x5++1/99x100= 1/2 + (1/2 - 1/3)+(1/3 - 1/4) +. +(1/99 - 1/100)= 1/2 +1/2 -1/3+1/3 -1/4+1/4+.+1/99 - 1/100= 1 - 1/100=99/100(*^__^* *^__^* *^__^*)有什么不明白可以对该题继续追问,随时在线等如果我的回答对你有帮助,请及时选为满意答案,谢谢

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