I'm trying work on my ability to break complex patterns down,
and in this case I'm trying to model the denominators of Lacsap's Fractions:
I managed to get the sequence that represents the denominators:
But now I want to convert it to a series in order to get rid of the tedious term D_n-1.
I guess I'm just not quite sure how to apply the sum identity to a parametric sequence:
The red is the answer that I've found works, but I don't know how to get to it.
When I simply substitute k, D_1, and D_k with snippets from the sequence, I get it wrong.