Answer
$\dfrac{15}{8}$
Work Step by Step
The lower limit of $m$ is $0$ and the upper limit is $3$.
Thus, evaluate the given summation from $m=0$ to $m=3$ to obtain:
$=\dfrac{1}{2^0} + \dfrac{1}{2^1}+\dfrac{1}{2^2}+\dfrac{1}{2^3}
\\=\dfrac{1}{1} + \dfrac{1}{2} + \dfrac{1}{4} + \dfrac{1}{8}$
Make the fraction similar using their LCD of $8$ to obtain:
$=\dfrac{8}{8} + \dfrac{4}{8} + \dfrac{2}{8} + \dfrac{1}{8}$
Add the fractions to obtain:
$=\dfrac{15}{8}$
