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 For which positive integers k is the series n=1(n!)5(kn)! convergent? \text { For which positive integers } k \text { is the series } \sum _ { n = 1 } ^ { \infty } \frac { ( n ! ) ^ { 5 } } { ( k n ) ! } \text { convergent? }


Definitions:

Financial Merger

A combination of two or more companies into one, with the primary goal of achieving financial synergy and efficiency.

Post-merger Cash Flows

The net cash inflows or outflows a company experiences following a merger or acquisition.

Operated Independently

Refers to entities or individuals carrying out activities or tasks without being directly controlled by another party.

Merger Activity

Refers to the process of combining two or more companies into a single entity, typically to achieve synergies, increase market share, or improve efficiency.

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