1. POTW 8
Solution
By: Doctor Proctor

2. 1 3 5 7 9 53
... 53
i i3 i5 i7 i 9
i
As we look at the denominators of each fraction,
It can be seen that there is a pattern of i, -i, i, -i
Therefore, we can simplify the expression as follows
1 3 5 7 9 53
...
i i i i i i
Then we can arrange these terms into pairs
1 3 5 7 49 51 53
...
i i i i i i i

3. In each pair there is a difference of 2i = (-2/i).
There are 13 pairs, with 53/i “leftover.”
So the sum can be written as:
2 53 26 53 27
13
i i i i i
27i