Problem: We need the sum of the number 1 to N. The N could be anything (100,200,500,33,21) like anything. What is the best approach to solve this little problem ? so there are multiple way to solve this problem. We will discuss 3 solution . 1. Recursive way : Using recursion we can solve this problem. Here is the solution The time complexity of this code is O(n) because it makes n recursive calls, each of which takes constant time. The space complexity is also O(n) because each recursive call adds a level to the call stack. The maximum depth of the recursion is n, so the maximum amount of space on the call stack is proportional to n. 2. Using loop Here we need 2 different variables in our code -- a variable where we can store the sum as we iterate through the values and add them (my_sum in my code), and another variable (i in my code) to iterate over the numbers from 0 to n. The time complexity of this code is O(n). The while loop runs n+1 times, and ...