Answer
$\dfrac{3}{2^2}+\dfrac{3^2}{2^3}+\dfrac{3^3}{2^4}+\dots+\dfrac{3^{50}}{2^{51}}$
Work Step by Step
We rewrite the given sum by expanding it: in each term $\dfrac{3^k}{2^{k+1}}$ substitute the value of $k$, where $k=1,2,3,\dots,50$:
$$\begin{align*}
\sum_{k=1}^{50}\dfrac{3^k}{2^{k+1}}&=\dfrac{3^1}{2^2}+\dfrac{3^2}{2^3}+\dfrac{3^3}{2^4}+\dots+\dfrac{3^{50}}{2^{51}}\\
&=\dfrac{3}{2^2}+\dfrac{3^2}{2^3}+\dfrac{3^3}{2^4}+\dots+\dfrac{3^{50}}{2^{51}}.
\end{align*}$$
We used dots in the sum because we cannot write all the $50$ terms of the sum.
