Question

Escreva os cinco primeiros termos de cada sequência d) an=(1/2) ^ n - 1 + n/2, com n e N
e) an = {n^2 + 1, se N for par
n^2 - 1, se N for ímpar , Com n e N
Por favor me ajudem !!!

Answer 1

Resposta:

d)

Se for aₙ=(1/2)ⁿ ⁻¹ + n/2, com n ∈ N

a₀=(1/2)⁰⁻¹+0/2 =(1/2)⁻¹+0 =2

a₁=(1/2)¹⁻¹+1/2= (1/2)⁰+1/2=1+1/2=3/2

a₂=(1/2)²⁻¹+2/2 = (1/2)¹+1 =1/2+1=3/2

a₃=(1/2)³⁻¹+3/2 =(1/2)²+3/2 =1/4+3/2 =1/4+6/4=7/4

a₄=(1/2)⁴⁻¹ +4/2 =(1/2)³ +2 =1/8+2=1/8+4/8=5/8

a₅=(1/2)⁵⁻¹+5/2 =(1/2)⁴+5/2 = 1/16+5/2 =(2+90)/32=23/8

e)

Se for aₙ=n²+1  se N for par

a₀==0²+1=1

a₂=2²+1=4+1=5

a₄=4²+1 =16+1=17

a₆=6²+1=36+1=37

a₈=8²+1=64+1=65

a₁₀=10²+1=100+1=101