Question

4. Encontre f(1), f(2), f(3) e f(4) sendo f a função recursiva dada por:

a) f(0) = 1 e, para n = 1, 2, ..., f(n + 1) = f(n) + 4

b) f(0) = 0 e, para n = 1, 2, ..., f(n + 1) = (n + 1)f(n) + 2

c) f(0) = 1 e, para n = 1, 2, ..., f(n + 1) = 2()

d) f(0) = 1, f(1) = −2 e, para n = 2, ..., f(n + 1) = $\frac{f(x)}{f(n - 1)}$

Answer 1

A) f(0+1)=f(0)+4
f(1)=5

f(1+1)=f(1)+4
f(2)=9

f(2+1)=f(2)+4
f(3)=13

f(3+1)=f(3)+4
f(4)=17

B) f(0+1)=(0+1).f(0)+2
f(1)=2

f(1+1)=(1+1).f(1)+2
f(2)=6

f(2+1)=(2+1).f(2)+2
f(3)=20

f(3+1)=(3+1).f(3)+2
f(4)=82


C) f(0+1)=2.f(0)
f(1)=2

f(1+1)=2.f(1)
f(2)=4

f(2+1)=2.f(2)
f(3)=8

f(3+1)=2.f(3)
f(4)=16