Lære Implementing Series in Python

In mathematics, series are sequences of numbers that follow a specific pattern. Two fundamental types of series are:

Arithmetic series, where each term increases by a constant difference;
Geometric series, where each term is multiplied by a constant ratio.

In Python, we can generate, manipulate, and visualize these series efficiently using lists and Matplotlib.

Defining an Arithmetic Series

An arithmetic series follows the formula:

Where:

a is the first term
d is the common difference
n is the number of terms
A list comprehension generates n terms of the sequence.
Each term increases by d from the previous term. Example Calculation:


              1234
            
def arithmetic_series(n, a, d):
    return [a + i * d for i in range(n)]

print(arithmetic_series(5, 2, 3))  # Output: [2, 5, 8, 11, 14]

Defining a Geometric Series

A geometric series follows the formula:

Where:

a is the first term
r is the common ratio (Each term is multiplied by r from the previous term.)
n is the number of terms


              1234
            
def geometric_series(n, a, r):
    return [a * r**i for i in range(n)]

print(geometric_series(5, 2, 2))  # Output: [2, 4, 8, 16, 32]

Plotting the Series in Python

To visualize the sequences, we plot them using matplotlib.


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import numpy as np
import matplotlib.pyplot as plt

# Define parameters
n = 10  
a = 2   
d = 3   
r = 2   

# Series generating functions
def arithmetic_series(n, a, d):
    return [a + i * d for i in range(n)]

def geometric_series(n, a, r):
    return [a * r**i for i in range(n)]

# Generate series
arith_seq = arithmetic_series(n, a, d)
geo_seq = geometric_series(n, a, r)

# Generate indices for x-axis
x_values = np.arange(1, n + 1)

# Create figure
plt.figure(figsize=(10, 5))

# Plot Arithmetic Series
plt.subplot(1, 2, 1)
plt.plot(x_values, arith_seq, 'bo-', label='Arithmetic Series')
plt.xlabel("n (Term Number)")
plt.ylabel("Value")
plt.title("Arithmetic Series: a + (n-1)d")
plt.grid(True)
plt.legend()

# Plot Geometric Series
plt.subplot(1, 2, 2)
plt.plot(x_values, geo_seq, 'ro-', label='Geometric Series')
plt.xlabel("n (Term Number)")
plt.ylabel("Value")
plt.title("Geometric Series: a * r^n")
plt.grid(True)
plt.legend()

# Show plots
plt.tight_layout()
plt.show()

1. How would you plot an arithmetic series in Python using `matplotlib`?

2. What will be the output of this code?

3. What Python function can you use to generate an arithmetic series with a first term of `2` and a common difference of `4`?

4. How do you define an arithmetic series function in Python?

How do you define an arithmetic series function in Python?

Select the correct answer

def arithmetic_series(n, a, d): 
    return [a + i * d for i in range(n)]

def arithmetic_series(n, a, d): 
    return [a * d**i for i in range(n)]

def arithmetic_series(n, a, d): 
    return [a - d**i for i in range(n)]

def arithmetic_series(n, a, d): 
    return [a * i + d for i in range(n)]

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Sektion 2. Kapitel 5

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Suggested prompts:

What is the difference between an arithmetic and a geometric series?

Can you explain how the Python functions for these series work?

How are these series used in real-world applications?

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In mathematics, series are sequences of numbers that follow a specific pattern. Two fundamental types of series are:

Arithmetic series, where each term increases by a constant difference;
Geometric series, where each term is multiplied by a constant ratio.

In Python, we can generate, manipulate, and visualize these series efficiently using lists and Matplotlib.

Defining an Arithmetic Series

An arithmetic series follows the formula:

Where:

a is the first term
d is the common difference
n is the number of terms
A list comprehension generates n terms of the sequence.
Each term increases by d from the previous term. Example Calculation:


              1234
            
def arithmetic_series(n, a, d):
    return [a + i * d for i in range(n)]

print(arithmetic_series(5, 2, 3))  # Output: [2, 5, 8, 11, 14]

Defining a Geometric Series

A geometric series follows the formula:

Where:

a is the first term
r is the common ratio (Each term is multiplied by r from the previous term.)
n is the number of terms


              1234
            
def geometric_series(n, a, r):
    return [a * r**i for i in range(n)]

print(geometric_series(5, 2, 2))  # Output: [2, 4, 8, 16, 32]

Plotting the Series in Python

To visualize the sequences, we plot them using matplotlib.


              1234567891011121314151617181920212223242526272829303132333435363738394041424344454647
            
import numpy as np
import matplotlib.pyplot as plt

# Define parameters
n = 10  
a = 2   
d = 3   
r = 2   

# Series generating functions
def arithmetic_series(n, a, d):
    return [a + i * d for i in range(n)]

def geometric_series(n, a, r):
    return [a * r**i for i in range(n)]

# Generate series
arith_seq = arithmetic_series(n, a, d)
geo_seq = geometric_series(n, a, r)

# Generate indices for x-axis
x_values = np.arange(1, n + 1)

# Create figure
plt.figure(figsize=(10, 5))

# Plot Arithmetic Series
plt.subplot(1, 2, 1)
plt.plot(x_values, arith_seq, 'bo-', label='Arithmetic Series')
plt.xlabel("n (Term Number)")
plt.ylabel("Value")
plt.title("Arithmetic Series: a + (n-1)d")
plt.grid(True)
plt.legend()

# Plot Geometric Series
plt.subplot(1, 2, 2)
plt.plot(x_values, geo_seq, 'ro-', label='Geometric Series')
plt.xlabel("n (Term Number)")
plt.ylabel("Value")
plt.title("Geometric Series: a * r^n")
plt.grid(True)
plt.legend()

# Show plots
plt.tight_layout()
plt.show()

1. How would you plot an arithmetic series in Python using `matplotlib`?

2. What will be the output of this code?

3. What Python function can you use to generate an arithmetic series with a first term of `2` and a common difference of `4`?

4. How do you define an arithmetic series function in Python?

How do you define an arithmetic series function in Python?

Select the correct answer

def arithmetic_series(n, a, d): 
    return [a + i * d for i in range(n)]

def arithmetic_series(n, a, d): 
    return [a * d**i for i in range(n)]

def arithmetic_series(n, a, d): 
    return [a - d**i for i in range(n)]

def arithmetic_series(n, a, d): 
    return [a * i + d for i in range(n)]

Var alt klart?

Tak for dine kommentarer!

Sektion 2. Kapitel 5

Implementing Series in Python

Defining an Arithmetic Series

Defining a Geometric Series

Plotting the Series in Python

1. How would you plot an arithmetic series in Python using matplotlib?

2. What will be the output of this code?

3. What Python function can you use to generate an arithmetic series with a first term of 2 and a common difference of 4?

4. How do you define an arithmetic series function in Python?

Awesome!

Implementing Series in Python

Defining an Arithmetic Series

Defining a Geometric Series

Plotting the Series in Python

1. How would you plot an arithmetic series in Python using matplotlib?

2. What will be the output of this code?

3. What Python function can you use to generate an arithmetic series with a first term of 2 and a common difference of 4?

4. How do you define an arithmetic series function in Python?

1. How would you plot an arithmetic series in Python using `matplotlib`?

3. What Python function can you use to generate an arithmetic series with a first term of `2` and a common difference of `4`?

1. How would you plot an arithmetic series in Python using `matplotlib`?

3. What Python function can you use to generate an arithmetic series with a first term of `2` and a common difference of `4`?