Taylor series representation problem During an exam recently, I was asked to prove that $-\ln(2) = \sum_{n=1}^\infty \dfrac{(-1)^n}{n\cdot2^n}$. But after fiddling around a lot, I kept reaching an argument that the sum actually equals $-\ln(1.5)$.
Was the exam incorrect?

The Taylor series of $ln(1 + x)$ about zero is the Mercator series:
$ln(1 + x) = \sum_{n=1}^\infty \dfrac{(-1)^{(n+1)}}{n}x^n$
If you set $x = 1$ you'll see there is an extra $\frac{1}{2^n}$ in their answer.
