<s>[INST] General term of the series Given the series:
$$\sqrt c + \sqrt{c\sqrt c} + \sqrt{c\sqrt{c\sqrt c}} + \ldots$$
where $0 < c < 1$
What is the general term of this series?
 [/INST] $a_1 = \sqrt{c} = c^{1/2}$, $a_2 = \sqrt{c\sqrt{c}} = \sqrt{c^{3/2}} = c^{3/4}$, $a_3 = \sqrt{c\sqrt{c\sqrt{c}}} = \sqrt{c \times c^{3/4}} = c^{7/4}$. In general, $$a_{n+1} = \sqrt{c a_{n-1}}$$ with $a_0 = 1$.
This gives us
 $a_n = c^{1-1/2^n}$
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