Question
सिद्ध कीजिए कि प्रत्येक अभिसारी अनुक्रम कौशी होता है।
Answer :
Word Count : 140
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मान लीजिए ({x_n}) एक अभिसारी अनुक्रम है और यह (x) पर अभिसरित होता है। तब परिभाषा के अनुसार, प्रत्येक (\varepsilon>0) के लिए एक प्राकृतिक संख्या (N) विद्यमान है, ऐसी कि सभी (n \ge N) के लिए (|x_n - x| < \varepsilon/2) हो। अब यदि (m \ge N) और (n \ge
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_______ ______.
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