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The Monotone Convergence Theorem is used after establishing that the sequence is both bounded below and non-increasing. It is invoked to guarantee the existence of a real limit $L$ for the sequence, which is a prerequisite for solving the limit equation.

Conditions: The sequence has been proven to be bounded from below.; The sequence has been proven to be non-increasing.

The Monotone Convergence Theorem is used after establishing that the sequence is both bounded below and non-increasing. It is invoked to guarantee the existence of a real limit $L$ for the sequence, which is a prerequisite for solving the limit equation.

Conditions: The sequence has been proven to be bounded from below.; The sequence has been proven to be non-increasing.