I just found it simpler to take a screenshot. I have no idea how to go about rearranging the equation like the solution does below.
Thanks.
Note that,
$\displaystyle \frac{\pi ^n}{3^{n+1}} = \frac{\pi^n}{3^n \cdot 3} = \frac{1}{3} \cdot \frac{\pi^n}{3^n} = \frac{1}{3} \cdot \left( \frac{\pi}{3} \right)^n$Thus,
$\displaystyle \sum_{n=0}^{\infty}\frac{\pi^n}{3^{n+1}} = \sum_{n=0}^{\infty} \frac{1}{3}\cdot \left( \frac{\pi}{3} \right)^n = \frac{1}{3}\sum_{n=0}^{\infty} \left( \frac{\pi}{3} \right)^n$
$\displaystyle 3^{n+1} = \underbrace{3\cdot 3\cdot ... \cdot 3}_{n+1 \text{ times }} = \underbrace{3\cdot 3\cdot ... \cdot 3}_{n\text{ times }}\cdot 3 = 3^n \cdot 3$.
In general, $\displaystyle x^{n+m} = x^n \cdot x^m$ where $\displaystyle n,m$ are positive integers.
You supposed to have known this in algebra. Not when learning Calculus.