(1)设二分之a=三分之b=四分之c=201120122013=k
则,a=2k,b=3k,c=4k
若m=4a+3b-4c分之3a+4b+c,
则m=(6k+12k+4k)/(8k+9k-16k)
=22k/k
=22
(2)
将22分成若干个整数的和,使他们的积最大
则应该将22尽量分成若干个2的和
即,22=2+2+……+2(11个2的和)
则,n=2×2……×2(11个2的积)=2的11次方
(3)
2x4分之1+4x6分之一+6x8分之一......+nx(n+2)分之一
=(1/2)×(1/2-1/4+1/4-1/6+1/6-1/8+……+1/n-1/(n+2))
=(1/2)×(1/2-1/(n+2))
=n/4(n+2)
=(2的11次方)/4(2的11次方+2)
=(2的8次方)/(1+2的10次方)
(1)a/2=b/3=c/4=201120122013=k
则a=2k,b=3k,c=4k
若m=(3a+4b+c)/(4a+3b-4c)(应该有括号吧?)
则m=(6k+12k+4k)/(8k+9k-16k)
=22k/k
=22
(2)
将22分成若干个整数的和,使他们的积最大
则应该将22分成6个3和一个4,他们的积最大为n=3^6x4=2916
(3)
1/(2x4)+1/(4x6)+1/(6x8)......+1/[n(n+2)](应该有括号吧?)
=(1/2){2/(2x4)+2/(4x6)+2/(6x8)......+2/[n(n+2)]}
=(1/2){(1/2-1/4)+(1/4-1/6)+(1/6-1/8)+……+[1/n-1/(n+2)]}
=(1/2){1/2-1/4+1/4-1/6+1/6-1/8+……+1/n-1/(n+2)}
=(1/2)(1/2-1/(n+2))
=(1/2)[(n+2)-2]/[2(n+2)]
=(1/2)n/[2(n+2)]
=n/[4(n+2)]
=2916/[4(2916+2)]
=2916/(4x2918)
=729/2918
1/2a= 1/4c 所以 4a= 2c
1/3b=1/4c 3b=9/4c
4a=3b-4c=2c+9/4c-4c=1/4c
同理 3a+4b+c =3/2c+ 3c+c=11/2c
m= 1/22