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UNIVESIDAD NACIONAL ABIERTA Y ADISTANCIA UNAD |
TALLER EJERCICIOS1.1 Y 1.2 |
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PRESENTADO POR : JEMERSON VARGAS RAMIREZ , ADELA, LEIDI |
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FECHA |
26/03/2011 |
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= > o
= > o
n(n+1)
n(n+1)
DESARROLLO
1. 2
2
Un=
= o
= o
0(0+1)
0(0+1)

2
2
U0=
1(1+1)
1(1+1)

= 1
= 1
2
2
U1=
2(2+1)
2(2+1)

= 3
= 3
2
2
U2=
= 3
= 3
3(3+1)3(3+1)

2
2
U3=
= 10
= 10
4(4+1)
4(4+1)

2
2
U4=
= 15
= 15
5(5+1)
5(5+1)

2
2
U4=
3
3

2. = > 5
= > 5
n-4
n-4
=
=
Un
=3
=3

3/1
3/1
=
=
3
3

5-4
5-4
U5=
1
1
=
=
3/2
3/2
=
=
3
3

6-4
6-4
U6=

1
1
=
=
3/3
3/3
=
=
3
3

7-4
7-4
U7=
3
3

0.75
0.75
=
=
3/4
3/4
=
=
8-4
8-4
U8=
10-4
10-4
3
3
0.50.5

=
=
3/6
3/6
=
=
U10=
0.99n
0.99n
n > 1
n > 1
=
=

3. Wn=

0.991
0.991
= 0.99
= 0.99

W1=

= 0.99*0.99=0.98
= 0.99*0.99=0.98
0.992
0.992

W2=

= 0.99*0.99*0.99=0.97
= 0.99*0.99*0.99=0.97
0.993
0.993

W3=

= 0.99*0.99*0.99*0.99=0.96
= 0.99*0.99*0.99*0.99=0.96

0.994
0.994
W4=

= 0.99*0.99*0.99*0.99*099=0.95
= 0.99*0.99*0.99*0.99*099=0.950.995
0.995
W5=

= 0.99*0.99*0.99*0.99*0.99=0.94
= 0.99*0.99*0.99*0.99*0.99=0.94

0.995
0.995
W6=

4. Un=Un-1+3
U1=U1-1+3=U.+3
U2=U2-1+3=U.+3+3
U3=U3-1+3=U.+3+3+3
Un=1+3n

5. Vn=3Vn-1 v0=2
V1=3-V0= v1=6
V2=3-V1 = 3(3.V0)=3(3.2)=32.vo=18
V3=3-V2 = 3(3.V1)=3(3) (3.V0) 33.vo=54
V4=3-V3 = 3(3.V2)=3(3(3 (3.V0) 34.vo=162
V5=3-V4 = 3(3.V3)=3(3(3)3)3.V0) 35.vo=4866. Vn=1/un-1 Vo =2
Vn=1/2 = ½
V1=1/vo=1/2
V2= (1/v1)=1/1/vo = vo/1 =VO =2
V3= V2 =1/1/v1 =1/1/1/v0 = v0/1 = v0= 2
V4= =1/v3 =1/1/v2=1/1/1/v1=1/1/1/1/v0=1/1/V0/1.1=1/1/1.V0/1.1=1/1/v0 - 1. V0 /1.1 =v0/1=2
Un =v0, v1, v2, v3
=2/1, ½, 2, ½, 2, ½
=21, 2-1, 21, 2-1,21,2-1
= v0, v1, v2, v3, v4, v5
=2(-1)0, 2(-1)1, 2(-1)2, 2(-1)3, 2(-1)5
=21, 2-1, 21, 2-1
1,3,9
1,3,9
Un = 2(-1)n7. Un=
30,31,32
30,31,32
Un=

V0, V1, V2
Un=3n

V3=33=27
V4=34=81
½, 1/5 ,1/10, 1/17….
½, 1/5 ,1/10, 1/17….

8. Un =
½, 1/12+1, 1/22, 1/22, 1/32, 1/42+1
v1, v2, v3, v4
Un =1/n2+1 = n>1
Comprobando
V3=1/32+1 =1/10
V4=1/42+1 =1/17
V5=1/52+1 =1/26
V6=1/62+1 =1/37
-5+5(355-1)

-5+5(355-1)

-5+4(355-1)

-5+4(355-1)

-5+3(355-1)

-5+3(355-1)

-5+2(355-1)-5+2(355-1)
(355-1)1
(355-1)1
-5-5
-5-5
Un=V0, V1, v2, V3, V4, v5

2/5,2
2/5,2
Un =-5+n(355-1)
9. .……
.……
,4
,4
2/5
2/5
,3
,3
2/5
2/5
2/5
2/5
Un=
0 2/5 , 1+1 2/5, 2+1 2/5, 3+1 2/5
0 2/5 , 1+1 2/5, 2+1 2/5, 3+1 2/5
Vn=
n+1 2/5 =n>0
n+1 2/5 =n>0

vn=



DESARROLLO DEEJERCICIO 1.2
1. =
=
n/2n+1
n/2n+1
Un
Un


V1
V1
= V1 = 1 /2 +1 = 1/3
= V1 = 1 /2 +1 = 1/3
1 /2(1)+1
1 /2(1)+1
=
=

= V2 = 2 /4 +1 = 2/5
= V2 = 2 /4 +1 = 2/5
2/2(2)+1
2/2(2)+1
V2=
V3= = V3 = 3 /6 +1 = 3/7
= V3 = 3 /6 +1 = 3/7
3/2(3)+1
3/2(3)+1
V2=
V4= = V4 = 4 /8 +1 = 4/9
= V4 = 4 /8 +1 =4/9
4/2(4)+1
4/2(4)+1
V2=
V5= = V5= 5 /10 +1 = 5/11
= V5= 5 /10 +1 = 5/11
5/2(5)+1
5/2(5)+1
V2=


Nota: la Sucesión creciente
2. Un = n/2n
Un = n/2n
Nota: la sucesión no monótona
Nota: la sucesión no monótona
V5= 5(-1)5 = 5(-1) V5 = -5 V5 =-5
V5= 5(-1)5 = 5(-1) V5 = -5 V5 =-5
V4= 5(-1)4 = 5(1) V4 =5 V4 =5
V4= 5(-1)4 = 5(1) V4 = 5 V4 =5
V3= 5(-1)3 = 5(-1) V3 = -5 V3 =-5
V3= 5(-1)3 = 5(-1) V3 = -5 V3 =-5
V2= 5(-1)2 = 5(1) V2 = 5 V2 =5
V2= 5(-1)2 = 5(1) V2 = 5 V2 =5
V1=
V1=
= 5(-1) v1 = -5 v1 =-5
= 5(-1) v1 = -5 v1 =-5
5(-1)1
5(-1)1
5(-1)n
5(-1)n
=
=
Un
Un...