Consider the problem of approximating

(B) ln[(1+x)/(1−x)] = 2 ∑ x

( 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

2. Which series do you

3. Write a code that computes the sum of

Your code should print out (on one line):

• the value of the input

• 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: Name: YOUR NAME Lab : 1 Date: ============================================================== - answers to 1, 2 ; ============================================================== - for each series: answer to 5 and what your code printed for that N ============================================================== - answer to 6 ; ======================================================== - your code (cleaned up!) Submit the file lab1.txt on Canvas (in plain text, no formating, no attachments please! )