I guess that demonstrates why it's important to have a REPL or a compiler available for the interviewee. (My computer wasn't available at the time that I wrote the comment.) I just wrote up my solution and confirmed that its terminating condition isn't correct.
It doesn't matter that it's not correct, the sad truth is that if you get that problem and write a loop and some math operators and update a variable for each run - you're in the top 10% of applicants!
There's a mindboggling amount of people applying for programming jobs who can't even do that!
A solution to this is looking at the distance from the current sum to the "boundary":
which works because this is an alternating series.