Question

Hallar los 5 primeros términos de cada una de las siguientes sucesiones.
Sn = {n} Sn ={3n-1} Sn = {(n+2)/n^2 }
Sn ={1/2^n } Sn = {(n+1)/2n} Sn = 〖(-1)〗^n

Answer 1

Respuesta:

Explicación paso a paso:

Sn = {n}

S₁ = 1           S₂ = 2         S₃ = 3       S₄ = 4         S₅ = 5

Sₙ = 1,2,3,4,5

Sn ={3n-1}

S₁ = 3(1)-1 = 3-1 = 2          S₂ = 3(2)-1 =6-1 = 5        S₃ = 3(3)-1 =9-1 = 8

S₄ = 3(4)-1 = 12-1 = 11       S₅ = 3(5)-1 = 15 -1 = 14

Sₙ = 2,5,8,11,14

Sn = {(n+2)/n^2 }

S₁ = (1+2)/1² = 3/1 = 3          S₂ = (2+2)/2² =4/4 = 1     S₃ = (3+2)/3² = 5/9

S₄ = (4+2)/4² = 6/16            S₅ = (5+2)/5² = 7/25

Sₙ = 3, 1, 5/9, 6/16, 7/25

Sn ={1/2^n }

S₁ = 1/2¹ = 1/2          S₂ = 1/2² = 1/4         S₃ = 1/2³ = 1/8         S₄ = 1/2⁴ = 1/16  

S₅ = 1/2⁵ =1/32

Sₙ = 1/2, 1/4, 1/8, 1/16, 1/32

Sn = {(n+1)/2n}

S₁ = (1+1)/2(1) = 2/2 = 1         S₂ = (2+1)/2(2) = 3/4      S₃ = (3+1)/2(3) = 4/6

S₄ = (4+1)/2(4) = 5/8           S₅ = (5+1)/2(5) = 6/10

Sₙ = 1, 3/4, 4/6, 5/8, 6/10

Sn = 〖(-1)〗^n

S₁ = (-1)¹ = -1        S₂ = (-1)² = 1      S₃ = (-1)³ = -1      S₄ = (-1)⁴ = 1    S₅ = (-1)⁵ = -1

Sₙ = -1, 1, -1, 1, -1