I am implementing a recursive code to sum of the sequence: x + x^2 / 2 + x^3 / 3... + x^n / n, i thought a setting combining two recursive functions, but is returning approximate values for n < 4, is very high for n >= 4, obviously is incorrect, but it was the best definition that i thought. Code Below:
def pot(x, n):
if n == 0: return 1
else:
return x * pot(x, n - 1)
def Sum_Seq (x, n):
if n == 1: return x
else:
return x + Sum_Seq(pot(x, n - 1), n - 1) / (n - 1)
If recursion is your mean and not your aim, you can use this function:
def polynom(x,n_max):
return sum(pow(x,n)*1./n for n in range(1, n_max + 1))
Then you get what you want:
x = 1
for i in range(5):
print polynom(x,i)
Out:
0
1.0
1.5
1.83333333333
2.08333333333
Your Sum_Seq()
function should be this:
def Sum_Seq (x, n):
if n == 1:
return x
else:
return pot(x, n)*1.0/n + Sum_Seq(x, n-1) # 1.0 is used for getting output as a fractional value.
NOTE: You don't need to make another recursive function calculate power. In python you can just do x**n
to get x to the power n.
In fact, I don't see why you need two recursive functions in this case. Simply use x**n
to calculate x
to the power n
:
def sum_seq(x, n):
if n == 1:
return x
else:
return (x**n/n) + sum_seq(x, n-1)
This works great in Python 3:
>>> power(10, 6)
Out[1]: 189560.0
Keep in mind that, in Python 2, the /
operator will infer whether you are doing an integer division or floating-point division. To guarantee your division will be the floating-point division in Python 2, just import the /
operator from Python 3 with:
from __future__ import division
or even cast your division to float:
float(x**n)/n
Your pot
function seems to perform the job of the **
power operator .
Maybe something like this will help -
In [1]: # x + x^2 / 2 + x^3 / 3... + x^n / n
In [2]: def sum_seq(x, n):
...: if n <= 0:
...: return 0
...: return (x**n)/n + sum_seq(x, n - 1)
...:
In [3]: sum_seq(10, 2)
Out[3]: 60.0
EDIT: I think the reason for the erroneous results in your code was this line -
return x + Sum_Seq(pot(x, n - 1), n - 1) / (n - 1)
Adding the Sum_Seq
to x, does not follow the pattern you've mentioned
Instead you can use simple linear recursion method
def lin_sum(s,n):
if n==0:
return 0
else:
return lin_sum(s,n-1)+s[n-1]
s=[1,2,3,4,5]
print(lin_sum(s,5))
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