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?

Indeed, we have $\ln(2)=\displaystyle\sum_{n=1}^\infty\dfrac1{n\cdot2^n}~,~$ while the expression they gave is $\ln\dfrac23~.$
