we got two groups of results: one with score of 0.75 (1 occurence) and
second with scores of 1 (2 occurences). First of all, the searched term
occurs exactly one in every document. So, following your equation they all
should get 1 score point. Yet they don't. Seems like they are different
factors included then. What's more, your equation will never succeed with
result of 0.7 for any integer k.