The nth harmonic number is defined non-recursively as: 1 +1/2 + 1/3 + 1/4 + + 1/n. come up with a recursive definition and use it to guide you to write a function definition for a double -valued function named harmonic that accepts an int parameters n and recursively calculates and returns the nth harmonic number. this is for myprogramminglab. com this is what i have double harmonic(int n) { int sum =0; if (n> 0) { sum=sum+(1/(harmonic( n-; } return sum; }

See the code below.

Explanation:

The nth armonic number is obtained from the following induction process:

And for the the n term we have this:

In order to create a code for the ne term we can use the following code using python:

# Code to find the nth armonic

# Function to find n-th Harmonic Number  

def armonicseries(n) :  

   # a1 = 1  

   harmonic = 1

   # We need to satisfy the following formulas:  

   # an = a1 + a2 + a3 ... +..... +an-1 + an-1 + 1/n  

   for i in range(2, n + 1) :  

       harmonic += 1 / i  

   return harmonic  

##############################

And then with the following instructions we find the solution for any number n.

   n = 3 # thats the number of n that we want to find

   print(round(armonicseries(n),5))

answer: when the substance contain the two parts (polar and non-polar) like soap.

explanation: