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(1+1/2)×(1%1/2)×(1+1/3)×(1%1/3)×...×(1+1/9)×(1%1/

(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*……*(1+1/9)*(1-1/9)=3/2*1/2*4/3*2/3**10/9*8/9=1/2*10/9=5/9

直接算不就好了..原式=3/2 * 4/3 * 5/4 ** 9/8 =9/2

(1-1/2*2)*(1-1/3*3)*(1-1/4*4)**(1-1/10*10)=(1+1/2)*(1-1/2)*(1+1/3)(1-1/3)*(1+1/4)(1-1/4)**(1+1/10)*(1-1/10)=(3/2)*(1/2)*(4/3)*(2/3)*(5/4)*(3/4)**(11/10)*(9/10)=[(1/2)*(2/3)*(3/4)**(9/10)]*[(3/2)*(4/3)*(5/4)**(11/10)]=(1/10)*(11/2)=11/20

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

20/11 (1+1/1*3)*(1+1/2*4)*(1+1/3*5)*(1+1/4*6)**(1+1/9*11) =4/3*9/8*16/15*25/24*36/35*49/48*64/63*81/80*100/99 =(2*3*4*5*6*7*8*9*10)^2/(1*2*3*4*5*6*7*8*9)(3*4*5*6*7*8*9*10*11) =20/11

题:1/1*2+1/2*3+1/3*4+…+1/9*10= 解:1/(1*2)=1/1-1/21/(2*3)=1/2-1/31/(3*4)=1/3-1/4::1/(9*10)=1/9-1/10 所以原式=(1/1-1/2)+……+(1/9-1/10)=9/10 题:(3-9/8+8/7)*21/13-169/56=13/7 题:0.12二循环+0.23三循环+0.34四循环+0.45五循环+

(1+1/2)*(1+1/3)*……*(1+1/9)=3/2*4/3*5/4*……*10/9=10/2=5

(1+1/2)*(1+1/4)*(1+1/6)**(1+1/10)*(1-1/3)*(1-1/5)**(1-1/9)=(1+1/2)*(1-1/3)*(1+1/4)*(1-1/5)(1+1/6)*(1-1/7)*(1+1/8)*(1-1/9)*(1+1/10)=3/2*2/3*5/4*4/5*7/6*6/7*9/8*8/9*11/10=11/10

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

简便算法:利用拆分法.原式=1-1/2=1/2-1/3+1/3-1/4+……+1/9-1/10 =1-1/10 =9/10拆分法: 1/[(n-1)*n]=1/(n-1)-1/n

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