Răspuns:
Explicație pas cu pas:
d)
6*n+1 / 3≤ 8*n +3/4
= se simplifica 6 cu 3 si ........8 cu 4
= 2n+1≤ 2n-+3
= 2n-2n≤3-1
n≤ 2
S={ 0,1,2 }
-
e)
7(n+1)<2(3n+5)
7n+7< 6n+10
7n-6n< 10-7
n< 3
S= { 0,1,2 }
-
f)
1/3n+1≤ 1/4
4*1≤3n+1
4-1≤3n
3≤3n
3n≥3
n≤3/3
n≥ 1
-
1/13≤1/3n+1
3n+1≤13
3n≤13-1
3n≤12
n≤12/3
n≤4
S={ 1,2,3,4 }
-
g)
1/2≤n+1 /n+2
n+2≤2*(n+1)
n+2≤2n+2
2n+2≥n+2
2n-n≥2-2
n≥0
-
n+1/n+2≤2/3
3*(n+1) ≤2(n+2)
3n+3≤ 2n+4
3n-2n≤4-3
n≤1
S= { 0,1}
-
h)
2012/2013≤ n+1/n+2
2012(n+2)≤2013(n+1)
2012n+4024 ≤2013n+2013
2013n+2013 ≥2012n+4024
2013n- 2012n≥4024-2013
n≥2011
-
2014(n+1)≤2013( n+2)
2014n+2014≤2013n+4026
2014n-2013≤ 4026-2014
n≤2012
S={ 2011, 2012}
-
-
l)
2/5≤2n+1/3n+4≤4/9
2*( 3n+4) ≤5*( 2n+1)
6n+8≤10n+5
10n+5≥6n+8
10n-6n≥8-5
4n≥3
n≥3/4
-
2n+1/ 3n+4≤4/9
9( 2n+1)≤4(3n+4)
18n+9≤12n+16
18n-12n≤16-9
6n≤7
n≤7/6
-
n≥⁶⁾3/4
n≤⁴⁾7/6
18/24<28/24
S= { 18/24 , 19/24 , 20 /24 , 21/24 ,22/24 ,23/24 , 24/24 ,25/24 ,26/24 ,27/24 , 28/24 }
