Program to Find Sum of Series 1^11!+2^22!+3^33!...+n^nn!

Python Program to Find Sum of Series 1^1/1!+2^2/2!+3^3/3!…+n^n/n!

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In the previous article, we have discussed Python Program to Find Sum of Series 1^1/1+2^2/2+3^3/3…+n^n/n
Given a number N and the task is to find the sum of series (1^1/1!+2^2/2!+3^3/3!…+N^N/N!) till the given number N in Python.

Examples:

Example1:

Input:

Given Number (Limit) = 6

Output:

The above series sum till the given number N{ 6 } =  109.00833333333333

Example2:

Input:

Given Number (Limit) = 15

Output:

The above series sum till the given number N{ 15 } =  541239.9325756768

Program to Find Sum of Series 1^1/1!+2^2/2!+3^3/3!…+n^n/n! in Python

Below are the ways to find the sum of series (1^1/1!+2^2/2!+3^3/3!…+N^N/N!) till the given number N in Python:

Method #1: Using For Loop (Static Input)

Approach:

  • Import math module using the import keyword.
  • Give the number N (Limit) as static input and store it in a variable.
  • Take a variable to say rsltseries_summ and initialize its value to 0.0 (Floating point number).
  • Take another variable to say factl_rslt and initialize its value to 1
  • Loop from 1 to the given number using the for loop.
  • Inside the loop, multiply the iterator value with the above factl_rslt and store it in the same variable.
  • Calculate the value of the iterator raised to the power itself and divided by the above factorial result using the pow() function.
  • Store it in another variable.
  • Add the above result to the rsltseries_summ and store it in the same variable.
  • Print the sum of series till the given number N.
  • The Exit of the Program.

Below is the implementation:

# Import math module using the import keyword.
import math
# Give the number N(limit) as static input and store it in a variable.
gvn_numb = 6
# Take a variable to say rsltseries_summ and initialize its value to 0.0
# (Floating point number)
rsltseries_summ = 0.0
# Take another variable to say factl_rslt and initialize its value to 1
factl_rslt = 1
# Loop from 1 to the given number using the for loop.
for itr in range(1, gvn_numb+1):
    # Inside the loop, multiply the iterator value with the above factl_rslt and
    # store it in the same variable.
    factl_rslt *= itr
    # calculate the value of the iterator raised to the power itself and
    # divided by the above factorial result using the pow() function.
    # Store it in another variable.
    a = pow(itr, itr) / factl_rslt
    # Add the above result to the rsltseries_summ and store it in the same variable.
    rsltseries_summ += a
# Print the sum of series till the given number N.
print(
    "The above series sum till the given number N{", gvn_numb, "} = ", rsltseries_summ)

Output:

The above series sum till the given number N{ 6 } =  109.00833333333333

Method #2: Using For loop (User Input)

Approach:

  • Import math module using the import keyword.
  • Give the number N (Limit) as user input using the int(input()) function and store it in a variable.
  • Take a variable to say rsltseries_summ and initialize its value to 0.0 (Floating point number).
  • Take another variable to say factl_rslt and initialize its value to 1
  • Loop from 1 to the given number using the for loop.
  • Inside the loop, multiply the iterator value with the above factl_rslt and store it in the same variable.
  • Calculate the value of the iterator raised to the power itself and divided by the above factorial result using the pow() function.
  • Store it in another variable.
  • Add the above result to the rsltseries_summ and store it in the same variable.
  • Print the sum of series till the given number N.
  • The Exit of the Program.

Below is the implementation:

# Import math module using the import keyword.
import math
# Give the number N (Limit) as user input using the int(input()) function and 
# store it in a variable.
gvn_numb = int(input("Enter some Random Number = "))
# Take a variable to say rsltseries_summ and initialize its value to 0.0
# (Floating point number)
rsltseries_summ = 0.0
# Take another variable to say factl_rslt and initialize its value to 1
factl_rslt = 1
# Loop from 1 to the given number using the for loop.
for itr in range(1, gvn_numb+1):
    # Inside the loop, multiply the iterator value with the above factl_rslt and
    # store it in the same variable.
    factl_rslt *= itr
    # calculate the value of the iterator raised to the power itself and
    # divided by the above factorial result using the pow() function.
    # Store it in another variable.
    a = pow(itr, itr) / factl_rslt
    # Add the above result to the rsltseries_summ and store it in the same variable.
    rsltseries_summ += a
# Print the sum of series till the given number N.
print(
    "The above series sum till the given number N{", gvn_numb, "} = ", rsltseries_summ)

Output:

Enter some Random Number = 15
The above series sum till the given number N{ 15 } = 541239.9325756768

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