# How do you write 3/2 + 5/4 + 9/8 + 17/16 + 33/32 in summation notation?

${\sum}_{1}^{n} \frac{{2}^{k} + 1}{2} ^ k$
The denominators are progressing geometrically while the numerators are always 1 greater than their denominators. For the ${k}^{t h}$ term in the series the denominator is ${2}^{k}$. This makes its numerator ${2}^{k} + 1$. The sum becomes
${\sum}_{1}^{n} \frac{{2}^{k} + 1}{2} ^ k$
where $n$ is the number of terms in the series.