Recursive sequence sum

Question

Recursive sequence sum

I am implementing a recursive code that sums the following sequence: x + x^2 / 2 + x^3 / 3... x^n / n, for this sum, I thought of a definition, combining two recursive functions, as follows low, but it is returning very high values, for n > 3.

def potencia(x, n):
    if n == 0: return 1
    else:
        return x * potencia(x, n - 1)

def Soma_Seq (x, n): 
    if n == 0: return 0
    else: 
        return x + Soma_Seq(potencia(x, n - 1), n - 1) / n

0

python-3.x recursão

Author: Marcelo de Sousa, 2017-08-19

Source

2 answers

score 1 · Answer 1

Given: Soma(x,n) = x + x^2 / 2 + x^3 / 3 + ... + x^n / n

Notice that:

Soma(x,n) = x + x^2 / 2 + x^3 / 3 + ... + x^n / n
#          |----------------------------|
Soma(x,n) =       Soma(x,n-1)           + x^n / n

Defining that, for n=1: Soma(x, 1) = x

def potencia(x, n):
    return (x**n)

def Soma_Seq (x, n): 
    if n == 1: return x
    else: 
        return Soma_Seq(x, n-1) + potencia(x, n)/n

We can also write the function potencia() recursively as follows:

def potencia(x, n):
    if n == 1: return x
    else:
        return x * potencia(x, n-1)

score 0 · Answer 2

We can use this answer for your question:

Recursive function that simulates a high number at a Power

def potencia(base, power, show_steps=True):
    """show_steps serve só para dizer 
    se amostrar os passos recursivos escritos ou não."""
    if power == 0: # caso base
        if show_steps:
            print(base, "^{0} = 1", sep="")        
        return 1
    else: # passo recursivo
        if show_steps:
            print(base, "^{", power, "} = ", base, " * ", base, "^{", power - 1, "}", sep="")
        return base * potencia(base, power - 1, show_steps)

def Soma_Seq (x, n): 
    if n == 0: return 0
    else: 
        return x + Soma_Seq(potencia(x, n - 1), n - 1) / n

I think it's a good starting point.