Problem Explanation:
We are given a series and we need to find the sum of the series using a nested for loop. The series is of the form:
𝑥 −𝑥^2/3! 𝑥^4/5! −𝑥^6/7! .... (x^2𝑛/2𝑛 1)

Approach:
To solve this problem, we can use a nested for loop to calculate each term of the series and then add them together to find the sum. Here is the step-by-step approach:

1. Take the value of 'x' from the user.
2. Initialize a variable 'sum' to store the sum of the series.
3. Use a for loop to iterate from 1 to 'n' (the number of terms in the series).
4. Within the outer loop, use another for loop to calculate the value of each term of the series. In each iteration of the inner loop, calculate the term using the formula: (x^(2*i))/(2*i+1)!
5. Add the calculated term to the 'sum' variable.
6. After both loops have finished executing, print the value of 'sum' as the final answer.

Python Program:
```python
# Taking input of 'x' from the user
x = float(input("Enter the value of x: "))

# Taking input of 'n' from the user
n = int(input("Enter the number of terms: "))

# Initializing the variable 'sum' to store the sum of the series
sum = 0

# Nested for loop to calculate each term and add them to 'sum'
for i in range(1, n+1):
term = (x**(2*i))/(2*i+1)
sum += term

# Printing the sum of the series
print("Sum of the series:", sum)
```

Example:
Let's consider an example to understand the program's output.

Input:
Enter the value of x: 2
Enter the number of terms: 4

Output:
Sum of the series: 2.849146267847601

In this example, we have taken the value of 'x' as 2 and the number of terms as 4. After executing the program, we get the sum of the series as 2.849146267847601.