Explanation

(a)
$\sum_{k = 1}^{5}{\frac{1^{3} + 2^{3} + ... + k^{3}}{1 + 3 + 5 + ... + (2k - 1)} = \sum_{k = 1}^{5}\frac{\left( \frac{k(k + 1)}{2} \right)^{2}}{k^{2}}}$
$= \sum_{k = 1}^{5}\frac{(k + 1)^{2}}{4}$
$= \frac{2^{2} + 3^{2} + 4^{2} + 5^{2} + 6^{2}}{4}$
$= \frac{4 + 9 + 16 + 25 + 36}{4}$
$= \frac{90}{4} = 22.5$