In the current issue of the Mathematical Gazette there is an article on slowly convergent series. There the tortoise challenges Achilles to sum the series:
to four significant figures.
Now far as I can see; this is an alternating series with terms of strictly decreasing absolute value which go to zero as goes to infinity and so it converges to a limit between and (between and ).
Also numerical experiments reassuringly suggest that the limit is
However the paper seems to think the sum . Which leaves me puzzled, what have I done wrong, or what could be the misprint in the expression for the series?