Answer
$\dfrac{63}{4}$
Work Step by Step
The sum of a geometric series can be found as:
$S_n=\dfrac{a_1}{1-r}$
where, $a_1$ denotes the first term and the $r$ is common ratio.
We are given that $\Sigma_{n=0}^{\infty} \dfrac{3^{n+2}}{7^n}$
This can be further written as: $\Sigma_{n=0}^{\infty}\dfrac{3^{n+2}}{7^n} =9+\dfrac{27}{7}+\dfrac{81}{49}+.......$
So, we have $a_1=9$ and $r=\dfrac{3}{7}$
Thus, the sum of a geometric series is:
$S_n=\dfrac{9}{1-\dfrac{3}{7}}=\dfrac{63}{4}$
