POTW 8 Solution

By: Doctor Proctor

3 5 7 9 53

1 3 5 7 9 53...

i i i i i 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

In each pair there is a difference of 2i. There are 13 pairs, so the sum can be written as:

2 53 26 53 2713

i i i i i

27i