Lab 1:  Taylor Series

Consider the problem of approximating ln(1.9) with ten digits of accuracy, using either of the following Taylor series:
(A)   ln(1−x) = − xk/k ,   −1≤x<1
(B)   ln[(1+x)/(1−x)] = 2 x2k−1/(2k-1) ,   −1<x<1

( both sums run from k=1 to infinity )   Write out a few terms to get a sense what each series is like.
Note that ln(1.9) is approximately 0.641853886172

1. To get ln(1.9), what value of x do you have to use in series (A) ? in series (B) ?

2. Which series do you expect to be more efficient for computing ln(1.9) ? (...before you do the rest !)

3. Write a code that computes the sum of N terms in series (A), for specified input N .
Your code should print out (on one line):
• the value of the input N (number of terms),
• the value of the sum obtained from the series,
• the error.

4. Modify your code to do the same for series (B) [ comment out and modify ].

5. How many terms do you need to find ln(1.9) with 10 digits accuracy using series (A) ?   series (B) ?

6. Which series is more efficient for computing ln(1.9) ? Briefly explain why.
```Create a PLAIN TEXT file "lab1.txt" containing:
Lab : 1 	Date:
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- answers to 1, 2 ;
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- for each series: answer to 5 and what your code printed for that N
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