Word Count : 301

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हमें यह दिखाना है कि दी गई श्रेणी \[ \sum_{n=1}^{\infty} \frac{x}{1 + n^2 x^2} \] \(\alpha < x < 1\) के लिए एकसमान रूप से अभिसारी (uniformly convergent) है। ### 1. श्रेणी की सीमा की जांच तर्क करने के लिए, हम उपरोक्त श्रेणी के सामान्य पद पर एक उपरी सीमा (upper bound) लगाने का प्रयास करते हैं। \[ \frac{x}{1 + _____ __________ _______ _______ ________.
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