<s>[INST] Why does this simplifies like that? 
I don't understand how do we simplify this fraction ? How does 3^n becomes 3^(n+1) and how does 1-(1/3) becomes 2 ???
Is there a general rule for this ?
 [/INST] Multiplying it by $3/3=1$ gives you
$$\frac{3^n}{1-(1/3)}\cdot \frac{3}{3}=\frac{3^n\cdot 3}{3(1-(1/3))}=\frac{3^{n+1}}{3-1}.$$
P.S. Multiplying a fraction by $1$ is sometimes helpful to make it simpler. For example, since $6/6=1$,
$$\frac{2/3}{5/6}=\frac{2/3}{5/6}\cdot \frac{6}{6}=\frac{(2/3)\cdot 6}{(5/6)\cdot 6}=\frac{4}{5}.$$
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