TRABAJO COLABORATIVO UNO ECUACIÓN DIFERENCIAL

TRABAJO COLABORATIVO UNO

MARLY JOHANA FIESCO RIVERA

GRUPO: 10410 – 88

TUTOR:

HAROLD PEREZ

UNIVERSIDAD NACIONAL ABIERTA Y A DISTANCIA - UNAD

PROGRAMA CÁLCULO DIFERENCIAL

TARQUI - HUILA

MARZO 2011

FASE 1

Hallar los 5 primeros términos de las siguientes sucesiones:

Un=(1/(3ⁿ^(+1) ) )ɳ≥1 = ( 1/9 ,1/(27 ) ,1/(81 ) ,1/243 ,1/729 … )

ɳ = 1 1/(3¹⁺¹) = 1/9

ɳ = 2 1/(3 ²⁺¹) = 1/3³ = 1/27

ɳ = 3 1/(3³⁺¹) =1/(3⁴) = 1/81

ɳ = 4 1/(3⁴⁺¹)= 1/(3⁵)= 1/243

ɳ = 5 1/(3⁵⁺¹)= 1/(3⁶)= 1/729

Un = ( 3/(3ⁿ^(-4) ) ) ɳ≥1=( -1, 1.5,0.20,0.125,0.16… )

ɳ = 1 3/(3( 1 )– 4 )= 3/(3-4) = -1/1= - 1

ɳ = 2 3/(3(2)- 4)= 3/(6 -4)= 3/2=1.5

ɳ = 3 1/(3 ( 3 )- 4)= 1/(9 -4)= 1/5=0.20

ɳ = 4 1/(3 ( 4 )- 4)= 1/(12 –4 )= 1/8=0.125

ɳ = 5 1/(2 ( 5 )– 4 )= 1/(30 -4)= 1/6=0.16

Wɳ = ( 1/(n -1) )ⁿ ɳ ≥2= ( 1,0.5,0.33,0.25,0.20… )

ɳ = 1 1/(2 -1)= 1/1=1

ɳ = 2 1/(3 –1 )= 1/2= 0.5

ɳ = 3 1/(4 -1)= 1/(3 ) = 0.33

ɳ = 4 1/(5 –1 )= 1/4 =0.25

ɳ = 5 1/(6 –1 )= 1/5 = 0.20

Identificar el término general dados el primer término y la relación de recurrencia.

U0= 2; Un= Un – 1 +1

U1= U0 +1=2 +1=3

U2 = U 2-1 +1= U1 +1=3 +1=4

U3= U 3 – 1 +2= U2 +1=4 +1=5

Uɳ= ɳ +2

U0=4; Uɳ = ( Uɳ -1)/5

U1= (U1 -1)/5= U0/5¹ = 4/5¹

U2 = ( U2 -1 )/5= ( U1 )/5=4 ( 1/5^2 )

U3 = (U3 -1)/5= U2/5=4 ( 1/5^3 )

U4= ( U4 -1 )/5= ( U3)/5 =4 ( 1/5^4 )

Uɳ=4 ( 1/(5 ) )ⁿ

ɳ ≥0

Wɳ = ( 2/(1 〖^-〗ɳ) ) ɳ≥2

Uɳ + 1 > Uɳ

Uɳ + 1 - Uɳ > 0

2/(1 - ( ɳ +1 ) ) ≥ 2/(1 - ɳ)

2/(1 - ɳ -1 ) ≥ 2/(1 - ɳ)

-2/ɳ ≥ 2/(1 - ɳ)

2/ɳ ≤ 2/(ɳ -1)

2 (ɳ - 1) ≤ 2 ɳ

2ɳ - 2 ≤ 2ɳ

2ɳ - 2ɳ ≤ 2

0 ≤ 2

Xɳ = 2 ⁻ⁿ

Xɳ = 1/(2 ⁿ)

Uɳ + 1 ˂ Uɳ

1/(2ⁿ ⁺¹) ˂ 1/2ⁿ

2 ⁿ ˂ 2ⁿ ⁺ ¹

Vɳ = ( (2ɳ +1)/ɳ )ɳ≥1

M = 1

Uɳ ≤ M

(2ɳ+1)/ɳ - 1

(2ɳ+1-ɳ)/ɳ= (ɳ+1)/ɳ

ɳ+1 ≤ 0 Y ɳ > 0

(ɳ +1)/ɳ ≤1

Para ɳ=0

FASE DOS

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