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This is a calculus question. Could you explain question 18 on
https://www.math.purdue.edu/php-scripts/courses/oldexams/serve_file.php?file=16600FE-F2016.pdf ?
I know the answer is D but don't know how to get there.
Please attach an image of your work as a reply.
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Every/any/each Calculus student knows (or must know - this knowledge is a pre-requisite) that
ln(1+y) = - + - + . . . (1)
for all real values y, |y| < 1. It is called " the Maclaurin series of f(y) = ln(1+y) ".
Replace (substitute) here y = -x^2. You will get
ln(1-x^2) = - - - - . . . (2)
Right side is your series with the sign "-, minus".
So, multiply both sides of identity (2) by (-1), and you will get the identity (D), which you need
= + + + + . . . (3)
Solved and explained.