(1-1/2+1/3-1/4.+1/1997-1/1998+1/1999)/[1/(1+1999)+1/(2+2000)+1/(3+2001).+1/(999+2997)+1/(1000+2998)]
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(1-1/2+1/3-1/4.+1/1997-1/1998+1/1999)/[1/(1+1999)+1/(2+2000)+1/(3+2001).+1/(999+2997)+1/(1000+2998)]
分子=1+1/2+1/3+...+1/1999 - 2*(1/2+1/4+...+1/1998)
=1+1/2+1/3+...+1/1999 - 1-1/2-1/3+...-1/999
=1/1000+1/1001+...+1/1999
分母=1/2000+1/2002+...+1/3998
=(1/1000+1/1001+...+1/1999)/2
所以原分数等于2
分子=1+1/2+1/3+...+1/1999 - 2*(1/2+1/4+...+1/1998)
=1+1/2+1/3+...+1/1999 - 1-1/2-1/3+...-1/999
=1/1000+1/1001+...+1/1999
分母=1/2000+1/2002+...+1/3998
=(1/1000+1/1001+...+1/1999)/2
分子=1+1/2+1/3+...+1/1999 - 2*(1/2+1/4+...+1/1998)
=1+1/2+1/3+...+1/1999 - 1-1/2-1/3+...-1/999
=1/1000+1/1001+...+1/1999
分母=1/2000+1/2002+...+1/3998
=(1/1000+1/1001+...+1/1999)/2
故原分数等于2
1/1*2+1/2*3+1/3*4...1/19*20=?
(1+19/105*1)+(1+19/105*2)+(1+19/105*3)+.+(1+19/105*19)+(1+19/105*20)
1+2+3+4.
1+2+3+4.
找规律19,1,17,2,15,3(),4.
1+2+3+4.+19+20怎样简便计算
1/2*1/3+1/3*1/4+1/4*1/5.+1/18*1/19+1/19*1/20
( 1+17/1)*(1+17/2)*(1+17/3)*.*(1+17/19)/(1+19/1)*(1+19/2)*(1+19/30*.*(1+19/17)=?
(1+19/105)+(1+19/105*2)+(1+19/105*3)+...+(1+19/105*20)
(1+1/2)*(1+1/3)*(1+1/4)*…*(1+1/18)*(1+1/19)*(1+1/20)
1/2×3+1/3×4+1/4×5+.+1/18×19+1/19×20等于?
求1/2*3+1/3*4+1/4*5+.+1/18*19+1/19*20
简算1/2*3+1/3*4+1/4*5+.+1/18*19+1/19*20
1/2×3+1/3×4+1/4×5+.+1/18×19+1/19×20等于?
1*2/1+2*3/1+.+18*19/1+19*20/1
1/1*2+1/2*3+.1/18*19+1/19*20=?
因为1/1*3=1/2*(1-1/3),1/3*5=1/2*(1/3-1/5),1/5*7=1/2*(1/5-1/7),.,1/17*19=1/2*(1/17-1/19)所以1/1*3+1/3*5+1/5*7+...+1/17*19=1/2*(1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+...+1/2*(1/17-1/19)=1/2*(1-1/3+1/3-1/5+1/5-1/7+...+1/17-1/19)=1/2*(1-1/19)=9/19(1
1/1*2+1/2*3+1/3*4+.+1/19*20+1/20*21