Error in Geometric series lecture?

[jstac]

Thanks to Richard Rivero for this:

I’m not sure you have the right Taylor series for G^{T+1} about g=0, somewhere down the page.

https://python.quantecon.org/geom_series.html

I would think it would be more something like:

[Smit-create]

Yeah, we can verify that using sympy:

>>> from sympy import series
>>> from sympy.abc import t, g
>>> f = (1 + g)**(t + 1)
>>> series(f, g)
1 + g*(t + 1) + g**2*t*(t + 1)/2 + g**3*t*(t - 1)*(t + 1)/6 + g**4*t*(t - 2)*(t - 1)*(t + 1)/24 + g**5*t*(t - 3)*(t - 2)*(t - 1)*(t + 1)/120 + O(g**6)