Question

need help in Python programming

Learning Objectives
You will learn how to create and analyze a recursive algorithm. You will learn about the difference between iterative and recursive algorithms.
Exercise 1: Recursion vs. iteration
a) Create a recursive function that finds the nth element A (n) in the formula A (n) = A (n-1) + 1 / n, A (1) = 1. The function should take the number n as a parameter. This represents series 1 + 1⁄2 + 1/3 + 1⁄4 + ... + 1 / n.
b) Find the recurrence equation for the function from Problem a)
c) Find the running time of the function from task a)
d) Create an iterative function to find the same element as in Problem a) using
dynamic programming.
e) Find the run time of the iterative function in O notation

Answer 1

a)

CODE

b)

The recurrence relation is given as:

T(n) = T(n-1) + c where c is a contsant

c)

On solving, we get,

T(n) = O(n)

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