👉 Blowing math, also known as blowing lemma or the "blowing lemma" in some contexts, is a fundamental result in real analysis that deals with the convergence of sequences and series. Informally, it states that if a sequence of positive real numbers is "blowing," meaning each term is strictly greater than any positive number raised to a sufficiently large power, then the original sequence must converge to zero. More formally, given a sequence \((a_n)\) of positive real numbers where \(a_n > C^n\) for all sufficiently large \(n\) and some constant \(C > 0\), it follows that \(\lim_{n \to \infty} a_n = 0\). This concept is crucial for understanding the behavior of sequences and series in analysis, ensuring that certain properties hold even when dealing with sequences that grow exponentially.
