[geom_series] Editorial Suggestions

[HumphreyYang]

Feedback from @SylviaZhaooo (Thanks!)

Content

• Revise the quotation marks in the quote “in economics, a little knowledge of geometric series goes a long way “
• "redeem note for gold or silver on demand" -> "redeem notes for gold or silver on demand"
• Add an intro to the Taylor series
• The signs of $\mathrm{r}$ and $\mathrm{g}$ are incorrect in the first line of expanding the equation of $p_0$
• Fill the gap in the derivations of $p_0$ in 10.5.3: 1. interpret why can approximate the $(T+1)^2$ into $(T+1)$ in the numerator of the second terms; 2. why $r g$ in the denominators disappear
• Typos and improvements in the derivations:

$$ \begin{aligned} p_0 & =\frac{x_0\left(1-1+(T+1)^2 r g\textcolor{red}{+}r(T+1)\textcolor{red}{-}g(T+1)\right)}{1-1+r-g+r g} \\ & =\frac{x_0(T+1)((T+1) r g+r-g)}{r-g+r g} \\ & \color{red} =\frac{x_0(T+1)(r-g)}{r-g+r g}+\frac{x_0 r g(T+1)^2}{r-g+r g} \\ & \approx \frac{x_0(T+1)(r-g)}{r-g}+\frac{x_0 r g(T+1)}{r-g} \\ & =x_0(T+1)+\frac{x_0 r g(T+1)}{r-g} \end{aligned} $$

• Shift "Back to the Keynesian multiplier" section as the exercise.