<s>[INST] plugging in terms of a sequence I am having some trouble understanding how to plug terms into the following sequence. I was given the following,
$$a_1=1, a_{n+1}=\frac{a_n}{\sqrt{n}}$$ for all n greater or equal to 1.
Plugging in terms we get the following,
$$a_1=1$$
$$a_2=a_1=1$$
$$a_3=\frac{a_2}{\sqrt{2}}=\frac{1}{\sqrt{2}}$$
$$a_4=\frac{a_3}{\sqrt{3}}=\frac{1}{\sqrt{6}}$$
How are they getting these terms $a_2,a_3,a_4$?
 [/INST] We have that for $n \in \mathbb Z^+$, $$a_{n+1} = \frac {a _n}{\sqrt {n}} \tag {1}$$
Thus, using the relation $(1)$ successively, we get, $$a_2 = a_{1+1} = \frac {a_1}{\sqrt {1}} = \frac {1}{1} =1 $$ $$a_3 = a_{2+1} = \frac {a_2}{\sqrt {2}} = \frac {1}{\sqrt {2}} $$ $$a_4 = a_{3+1 } = \frac {a_3}{\sqrt {3}} = \frac {1}{\sqrt {2}\times \sqrt {3}} = \frac {1}{\sqrt {6}} $$
Hope it helps. 
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