Question
कॉशी अनुक्रम को परिभाषित कीजिए। सिद्ध कीजिए कि अनुक्रम , जहाँ
कॉशी है।
Answer :
Word Count : 284
कॉशी अनुक्रम (Cauchy Sequence) की परिभाषा इस प्रकार है: अनुक्रम \( (a_n) \) को कॉशी अनुक्रम कहा जाता है यदि \(\forall \epsilon > 0\), एक \(N \in \mathbb{N}\) ऐसा है कि जब \(m, n > N\) हों, तब \(|a_n - a_m| < \epsilon\). दिया गया अनुक्रम \(a_n = \frac{3^2}{x^2 + 2^2} = \frac{9}{x^2 + 4}\) है। _________ ___ _________ _________ _____ _________.
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कॉशी अनुक्रम (Cauchy Sequence) की परिभाषा इस प्रकार है: अनुक्रम \( (a_n) \) को कॉशी अनुक्रम कहा जाता है यदि \(\forall \epsilon > 0\), एक \(N \in \mathbb{N}\) ऐसा है कि जब \(m, n > N\) हों, तब \(|a_n - a_m| < \epsilon\). दिया गया अनुक्रम \(a_n = \frac{3^2}{x^2 + 2^2} = \frac{9}{x^2 + 4}\) है। _________ ___ _________ _________ _____ _________.
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