Program to Find the Sum of Series 1+X+X^3...+X^N

Python Program to Find the Sum of Series 1+X+X^3…+X^N

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In the previous article, we have discussed Python Program to Find Sum of Series 1/2-2/3+3/4-4/5+5/6…+N/N+1

Given the numbers, N and X and the task is to find the sum of the given series (1+X+X^3…+X^N) for the given numbers in Python.

Examples:

Example1:

Input:

Given Number = 4
Given X value =  8

Output:

The total sum of the series till the given number N and x value { 4 8 } =  520

Example2:

Input:

Given Number = 5
Given X value = 11

Output:

The total sum of the series till the given number N and x value { 5 11 } =  162393

Program to Find the Sum of Series 1+X+X^3…+X^N in Python

Below are the ways to find the sum of the given series (1+X+X^3…+X^N) for the given numbers in Python :

Method #1: Using While Loop (Static Input)

Approach:

  • Give the number N as static input and store it in a variable.
  • Give the value of X as static input and store it in another variable.
  • Take a variable say resltsum which gives the sum of the given series till N and initialize its value to 0.
  • Take another variable say k and initialize its value with 1.
  • Loop until the value of k is less than or equal to the given number using the while loop.
  • Inside the loop, calculate the value of X raised to the power k using the pow() function and store it in a variable say p.
  • Add the above value of p to the resltsum and store it in the same variable.
  • Increment the value of k by 2 and store it in the same variable k.
  • Print the resltsum value which is the result of the series till the given Number N.
  • The Exit of the Program.

Below is the implementation:

# Give the number N as static input and store it in a variable.
gvn_numb = 4
# Give the value of x as static input and store it in another variable.
gvn_x_val = 8
# Take a variable say resltsum which gives the sum of the given series till N and
# initialize its value to 0.
resltsum = 0
# Take another variable say k and initialize its value with 1.
k = 1
# Loop until the value of k is less than or equal to the given number using the while loop.
while(k <= gvn_numb):
    # Inside the loop, calculate the value of X raised to the power k using the pow() function
    # and store it in a variable say p.
    p = pow(gvn_x_val, k)
 # Add the above value of p to the resltsum and store it in the same variable.
    resltsum += p
 # Increment the value of k by 2 and store it in the same variable k.
    k += 2
# Print the resltsum value which is the result of the series till the given Number N.
print(
    "The total sum of the series till the given number N and x value {", gvn_numb, gvn_x_val, "} = ", resltsum)

Output:

The total sum of the series till the given number N and x value { 4 8 } =  520

Method #2: Using While loop (User Input)

Approach:

  • Give the number N as user input using the int(input()) function and store it in a variable.
  • Give the value of X as user input using the int(input()) function and store it in another variable.
  • Take a variable say resltsum which gives the sum of the given series till N and initialize its value to 0.
  • Take another variable say k and initialize its value with 1.
  • Loop until the value of k is less than or equal to the given number using the while loop.
  • Inside the loop, calculate the value of X raised to the power k using the pow() function and store it in a variable say p.
  • Add the above value of p to the resltsum and store it in the same variable.
  • Increment the value of k by 2 and store it in the same variable k.
  • Print the resltsum value which is the result of the series till the given Number N.
  • The Exit of the Program.

Below is the implementation:

# Give the number N as user input using the int(input()) function and
# store it in a variable.
gvn_numb = int(input("Enter some Random Number = "))
# Give the value of X as user input using the int(input()) function and
# store it in another variable.
gvn_x_val = int(input("Enter some Random Number = "))
# Take a variable say resltsum which gives the sum of the given series till N and
# initialize its value to 0.
resltsum = 0
# Take another variable say k and initialize its value with 1.
k = 1
# Loop until the value of k is less than or equal to the given number using the while loop.
while(k <= gvn_numb):
    # Inside the loop, calculate the value of X raised to the power k using the pow() function
    # and store it in a variable say p.
    p = pow(gvn_x_val, k)
 # Add the above value of p to the resltsum and store it in the same variable.
    resltsum += p
 # Increment the value of k by 2 and store it in the same variable k.
    k += 2
# Print the resltsum value which is the result of the series till the given Number N.
print(
    "The total sum of the series till the given number N and x value {", gvn_numb, gvn_x_val, "} = ", resltsum)

Output:

Enter some Random Number = 5
Enter some Random Number = 11
The total sum of the series till the given number N and x value { 5 11 } = 162393

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