Question

Please let me know if you have any questions. Thanks in advance!

We want to develop a code that calculates In(1 - x) =- on the interval -1<x<1. First, understand what this notation represents. The capital sigma (2) indicates that a summation of terms is to be performed. (The term summation still applies even though all the terms are negative.) We are also given the prototype term written in terms of x and n. The notation also tells us that n is to start at a value of 1 and increase by 1 as the value of n heads toward infinity. The following shows how this series summation should be calculated: Inc. -1)=-69-0-0-0- In(1 – x) = - How do we know when to stop? First, we do not need to calculate an infinite number of terms. We'll soon see that four or five terms provides an acceptable answer. We could specify a set number of terms, but a more acceptable way of performing this calculation is to use a loop of some sort and a tolerance value that lets us know when to stop. We will accumulate a sum of terms until we calculate a term value that is less than the specified tolerance value. This will make more sense if we look at a Python example. Two cases are shown: 1. Case 1: User enters x in the interval -1 <x< 1 and the number of terms 2. Case 2: User enters x in the interval -1<x< 1 and the acceptable tolerance. a. You can experiment with TOL values between 1e-01 and 1e-08

Answer 1

 #CASE 1 x=float(input("Enter Value of x between -1 and 1: ")) #Takes input for value of x n=int(input("Enter number of terms: ")) #Takes input for number of terms sum=0 #Initialises sum which will store the summation for i in range(1,n+1): #this loop will run for n number of times from 1 to n sum+=(pow(x,i)/i) #(x^i)/i is added to sum each time loop runs print(-sum) #finally prints sum with negative sign as ln(1-x)=-summation

 #CASE 2 x=float(input("Enter Value of x between -1 and 1: ")) #Takes input for value of x t=float(input("Enter the tolerance limit: ")) #Takes input for tolerance limit sum=0 #Initialises sum which will store the summation i=1 #initialises i which is used for increneting the exponent and divisor while(abs(pow(x,i)/i)>t): #The loop will run till the difference between sum and sum+next term is greater than tolerance limit sum+=(pow(x,i)/i) i+=1 print(-sum) #finally prints sum with negative sign as ln(1-x)=-summation