 # 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:

### 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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