✔ 最佳答案
1.1*2*3*…*100/60^100化為最簡分數n/m,以標準分解式表示,則m=2^a*3^b
,則a+b的值為?
(A)55 (B)54 (C)53 (D)52
Sol
[100/2]=50
[50/2]=25
[25/2]=12
[12/2]=6
[6/2]=3
[3/2]=1
50+25+12+6+3+1=97
[100/3]=33
[33/3]=11
[13/3]=4[4/3]=1
33+11+4+1=49
1*2*3*…*100/60^100
=A*2^97*3^49/(2^100*3^100)
=A/(2^3*3^51)
a+b=3+51=54
(B)
2.n1,n2,...nk為正整數,若720=2^n1+2^n2+...+2^nk,n1+n2+...+nk的最小值為?
(A)26 (B)27 (C)28 (D)29
Sol
2^9=512
n1=9
720-512=208
2^7=128
208-128=80
n2=7
2^6=64
n3=6
80-64=16
2^4=16
n4=4
9+7+6+4=26
(A)
3.下列哪一個數落在從1/4到3/4之間1/3的位置?
(A)1/2 (B)5/12 (C)1/3(D)2/3
Sol
1/4+(3/4-1/4)*(1/3)=1/4+(2/4)*(1/3)
=1/4+1/6
=3/12+2/12
=5/12
(B)
2014-06-16 08:25:04 補充:
100!=(2^97)*(3^49)*(5^....)*...*97