Related question: Finding the first 5 terms of a Maclaurin Series using division?
Hello, I'm having trouble finding the first four terms of the Maclaurin series for the following function (using long division): $$ {\mathrm{tan} ^{-1} x \over 1+x} $$
It is already established that $\mathrm{tan} ^{-1} x = x - {x^{3} \over 3} + {x^{5} \over 5} - {x^{7} \over 7} + {x^{9} \over 9} - \cdots$ , so dividing this by $1+x$ gives me
$$ x - x^{2} + {2 \over 3} x^{3} - {2 \over 3} x^{4} + {13 \over 15} x^{5} - \cdots $$
But the book expects the following answer:
$$ x + x^{2} - {x^{3} \over 3} + {x^{4} \over 3} - \cdots $$
which isn't even remotely close to my current result.
Any help would be greatly appreciated. Thanks in advance.
