Python Program to Find Sum of Series 1/2!+2/3!+3/5!+.....N/(N+1)!

In the previous article, we have discussed Python Program to Find Sum of Series 5^2+10^2+15^2+…..N^2
Given a number N and the task is to find the sum of series (1/2!+2/3!+3/5!+…..N/(N+1)!) 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 } =  0.9998015873015872

Example2:

Input:

Given Number (Limit) = 13

Output:

The above series sum till the given number N{ 13 } =  0.9999999999885293

Program to Find Sum of Series 1/2!+2/3!+3/5!+…..N/(N+1)!

Below are the ways to find the sum of series (1/2!+2/3!+3/5!+…..N/(N+1)!) till the given number N in Python:

Using While Loop (Static Input)
Using While loop (User Input)

Method #1: Using While 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 itr and initialize its value to 1.
Take another variable to say rsltseries_summ and initialize its value to 0.0 (Floating point number).
Loop until the above-declared variable itr value is less than or equal to the given number using the while loop.
Calculate the factorial of itr+1 using the math.factorial() method and store it in another variable.
Calculate the value of itr divided by the above result factorial and convert it into float using the float() function.
Store it in another variable.
Add the above result to the rsltseries_summ and store it in the same variable.
Increment the above itr value by 1.
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 itr and initialize its value to 1.
itr = 1
# Take a variable to say rsltseries_summ and initialize its value to 0.0
# (Floating point number)
rsltseries_summ = 0.0
# Loop until the above-declared variable itr value is less than or equal to the
# given number using the while loop.
while(itr <= gvn_numb):
    # Calculate the factorial of itr+1 using the math.factorial() method and
    # store it in another variable.
    factrl = math.factorial(itr+1)
    # Calculate the value of itr divided by the above result factorial and convert it
    # into float using the float() function.
    # Store it in another variable.
    p = float(itr/factrl)
    # Add the above result to the rsltseries_summ and store it in the same variable.
    rsltseries_summ += p
    # Increment the above itr value by 1.
    itr += 1
# 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 } =  0.9998015873015872

Method #2: Using While 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 itr and initialize its value to 1.
Take another variable to say rsltseries_summ and initialize its value to 0.0 (Floating point number).
Loop until the above-declared variable itr value is less than or equal to the given number using the while loop.
Calculate the factorial of itr+1 using the math.factorial() method and store it in another variable.
Calculate the value of itr divided by the above result factorial and convert it into float using the float() function.
Store it in another variable.
Add the above result to the rsltseries_summ and store it in the same variable.
Increment the above itr value by 1.
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 itr and initialize its value to 1.
itr = 1
# Take a variable to say rsltseries_summ and initialize its value to 0.0
# (Floating point number)
rsltseries_summ = 0.0
# Loop until the above-declared variable itr value is less than or equal to the
# given number using the while loop.
while(itr <= gvn_numb):
    # Calculate the factorial of itr+1 using the math.factorial() method and
    # store it in another variable.
    factrl = math.factorial(itr+1)
    # Calculate the value of itr divided by the above result factorial and convert it
    # into float using the float() function.
    # Store it in another variable.
    p = float(itr/factrl)
    # Add the above result to the rsltseries_summ and store it in the same variable.
    rsltseries_summ += p
    # Increment the above itr value by 1.
    itr += 1
# 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 = 13
The above series sum till the given number N{ 13 } = 0.9999999999885293

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