Calculo Diferencial

0, 1, 2, 3, 4

U_(0 )= {(0(0-1))/3} =0

U_(1 )= {(1(1-1))/3} =0

U_(2 )= {(2(2-1))/3} =2/3

U_(3 )= {(3(3-1))/3} =6/3 =2

U_(4 )= {(4(4-1))/3} =12/3=4

= {0,0,2/3 ,2,4}

U_(n )= {4/(n-3)}_(n≥4)

U_(4 )= {4/(4-3)}_(n≥4)=4

U_(5 )= {4/(5-3)}_(n≥4)=2

U_6= {4/(6-3)}_(n≥4)=4/3

U_(7 )= {4/(7-3)}_(n≥4)=1

U_(8 )= {4/(8-3)}_(n≥4)=4/5

U_(9 )= {4/(n-3)}_(n≥4)=2/3

U_(n )= {4/(n-3)}_(n≥4) = {4,2,4/3,1,4/5,2/3}

U_(n )= {1,3,9,19}

U_(n )= 1+2 〖(n-1)〗^2

V_(0 )=1

V_(n )= V_(n-1)+3

V_(1 )= V_(1-1)+3

V_(1 )= V_0+3

V_(1 )= 1+3

V_(1 )=4

V_(2 )= V_(2-1)+3

V_(2 )= V_1+3

V_2= 4+3

V_2=7

V_3= V_(3-1)+3

V_(3 )= V_2+3

V_3= 7+3

V_3=10

V_3= V_(3-1)+3

V_(3 )= V_2+3

V_3= 7+3

V_3=10

V_4= V_(4-1)+3

V_(4 )= V_3+3

V_4= 10+3

V_4=13

Termino General

3n-2

Valor inicial V0 = 2

Relación de recurrencia

Vn = 3Vn-1

V1 = 3V1-1

V1 = 3V0

V1 = 3(2)

V1 = 6

V2 = 3V2-1

V2 = 3V1

V2 = 3(6)

V2 = 18

V3 = 3V3-1

V3 = 3V2

V3 = 3(18)

V3 = 54

Termino General

Vn = 2 * 3n-1

U_n= {2n^3+ n+2}_(n≥0)

{2(0)^3+0+2}=2

{2(1)^3+1+2}=5

{2(2)^3+2+2}=20

{2(3)^3+3+2}=59

{2(4)^3+4+2}=130

= {2,5,20,59,130} si es creciente porque va aumentando el valor de cada termino.

U_n= {1/n}_(n≥1)

U_1= {1/1}=1

U_2= {1/2}=1/2

U_3= {1/3}=1/3

Es estrictamente decreciente porque a partir del primer término, los demás van decreciendo sin llegar a repetirse.

Valor inicial W0 = 5

Relación de recurrencia

Wn+1 = W0 - (e + 3)

e = 2.71

W1 = W0 – (e+3)

W1 = 5 – e + 3 = 2-e = 0.71

W2 = W1 – (e + 3) = 2- e – e – 3

= 1-2e = -6.42

W3 = W2 – (e + 3) = -1- 2e – e – 3

= -4 -3e = 12,13

W4 = W3 – (e + 3) = 4- 3e – e – 3

= -7 –e =-17,84

Es decreciente por lo tanto es monótona.

V_0= {8(-1)^n }_(n≥0)

V_0= {8(-1)^0 }

V_0= -8

V_1= {8(-1)^1 }

V_1= -8

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