What exactly is Stop in this question and how do I get the sum?-CodePudding

Problem Statement

Edit: I have transcribed the image as suggested although I think some terms are better shown in the picture if anything is unclear here;

This function takes in a positive integer n and returns the sum of the following series Sn, as long as the absolute value of each term is larger than stop.

Sn= 1 − 1/2 1/3 − 1/4 ... (−1)^{n 1}/n ...

You can assume that stop is a float value and 0 < stop < 1.

You need not round the output.

For example, if stop = 0.249, then Sn is evaluated with only four terms.

Sn = 1 − 1/2 1/3 − 1/4

For example, if stop = 0.199, then Sn is evaluated with only five terms.

Sn = 1 − 1/2 1/3 − 1/4 1/5

The built-in function abs() is useful. You should use a while loop.

Test cases:

print( alternating_while(0.249) )
print( alternating_while(0.199) )

gives:

0.5833333333333333  
0.7833333333333332

Now for this question, I want to get the sum of this series based on the conditions stipulated in the question.

My problem is I don't understand how to type the formula given in the question because I'm not familiar with how the while-loop works. Can someone instruct me on how to?

def alternating_while(stop):
    total = 0
    n = 1
    term = 1
    while abs(term) > stop:
        total= (-1) ** (n   1) / n   alternating_while(n - 1)
        return total

CodePudding user response：

No reason to use recursion as it wasn't mentioned as a requirement. Just check the term in the while loop for the stop condition:

Python 3.8 (for the := operator):

def alternating_while(stop):
    n = 1
    total = 0
    while abs(term := (-1)**(n 1)/n) > stop:
        total  = term
        n  = 1
    return total

print(alternating_while(0.249))
print(alternating_while(0.199))

Output:

0.5833333333333333
0.7833333333333332

Pre-Python 3.8 version:

def alternating_while(stop):
    n = 1
    total = 0
    while True:
        term = (-1)**(n 1)/n
        if abs(term) <= stop:
            break
        total  = term
        n  = 1
    return total

Or:

def alternating_while(stop):
    n = 1
    total = 0
    term = (-1)**(n 1)/n
    while abs(term) > stop:
        total  = term
        n  = 1
        term = (-1)**(n 1)/n    # redundant
    return total

CodePudding user response：

The key is "alternating". You can just increment the current denominator one at a time. If it is odd, you add. Otherwise, you subtract. abs is not really required; I'm not sure why they would mention it.

def alternating_while(stop):
    total = 0
    denom = 1
    while 1/denom > stop:
        if denom & 1:
            total  = 1/denom
        else:
            total -= 1/denom
        denom  = 1
    return total

print(alternating_while(0.249))
print(alternating_while(0.199))

Output:

0.5833333333333333
0.7833333333333332

CodePudding user response：

You need to cycle between adding and subtracting. The itertools module has a very helpful cycle class which you could utilise thus:

from itertools import cycle
from operator import add, sub

def get_term(d=2):
    while True:
        yield 1 / d
        d  = 1

def calc(stop=0.199):
    c = cycle((sub, add))
    term = get_term()
    Sn = 1
    while (t := next(term)) > stop:
        Sn = next(c)(Sn, t)
    return Sn

print(calc())

Output:

0.6936474305598223

Note:

The reference in the problem statement to absolute values seems to be irrelevant as no terms will ever be negative