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Fix Taylor series about g=0 in Geometric series lecture #254

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Aug 28, 2022
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Fix Taylor series about g=0 in Geometric series lecture #254

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3 changes: 1 addition & 2 deletions lectures/geom_series.md
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Expand Up @@ -626,7 +626,7 @@ $$
Similarly, applying the Taylor series to $G^{T+1}$ about $g=0$:

$$
(1+g)^{T+1} = 1+(T+1)g(1+g)^T+(T+1)Tg^2(1+g)^{T-1}+\dots \approx 1+ (T+1)g
(1+g)^{T+1} = 1+(T+1)g+\frac{T(T+1)}{2!}g^2+\frac{(T-1)T(T+1)}{3!}g^3+\dots \approx 1+ (T+1)g
$$

Thus, we get the following approximation:
Expand Down Expand Up @@ -920,4 +920,3 @@ plt.show()
Notice here, whether government spending increases from 0.3 to 0.4 or
investment increases from 0.3 to 0.4, the shifts in the graphs are
identical.