- In this question you may assume the results for
$$\sum _ { r = 1 } ^ { n } r ^ { 3 } , \sum _ { r = 1 } ^ { n } r ^ { 2 } \text { and } \sum _ { r = 1 } ^ { n } r$$
- Show that the sum of the cubes of the first \(n\) positive odd numbers is
$$n ^ { 2 } \left( 2 n ^ { 2 } - 1 \right)$$
The sum of the cubes of 10 consecutive positive odd numbers is 99800
- Use the answer to part (a) to determine the smallest of these 10 consecutive positive odd numbers.