Respuesta :
Answer:
An = A(n−1) + A(n−2) + 2 A(n−5) + 2 A(n−10) + A( n−20) + A(n−50) +A (n−100)
Step-by-step explanation:
given data
coins currency values = 1 peso, 2 pesos, 5 pesos, and 10 pesos and bills with values of 5 pesos, 10 pesos, 20 pesos, 50 pesos, and 100 pesos
solution
we take here 1 pays a certain amount of pesos n
so we get here recurrence relation that is express as here
when here 1 pays
To pay 1 peso so then n-1 peso
To pay 2 peso so then n-2 peso, when n≥2
To pay 5 peso so then n-5 peso, when n≥5
To pay 10 peso so then n-10 peso, when n≥10
To pay 5 peso bill so then n-5 peso, when n≥5
To pay 10 peso bill so then n-10 peso, when n≥10
To pay 20 peso bill so then n-20 peso, when n≥20
To pay 50 peso bill so then n-50 peso, when n≥50
To pay 100 peso bill so then n-100 peso, when n≥100
so that here we take A(o) = 1
and we take here n-1, n-2, n-3, n-4 ........ are subscript of A when we take patterns for every part of recurrences
so recurrence relation
A(n) = A(n-1) + A(n-2) + A(n-5) + A(n−10) + A(n-5) + A(n-10) + A(n−20) + A(n−50) + A(n−100)
simpyfy it we get
An = A(n−1) + A(n−2) + 2 A(n−5) + 2 A(n−10) + A( n−20) + A(n−50) +A (n−100) for n≥101
