Word Count : 299

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समस्या को हल करने के लिए, हमें निम्नलिखित सीमा की गणना करनी है: \[ \lim_{n\rightarrow\infty}\left[\frac{1}{\sqrt{2n-1^2}}+\frac{1}{\sqrt{4n-2^2}}+\frac{1}{\sqrt{6n-3^2}}+\cdots+\frac{1}{\sqrt{2n(n)-n^2}}\right] \] इस सीमा को हल करने के लिए, हम इसे एक समाकल (integral) के रूप में व्यक्त करेंगे। ### चरण 1: सीमा को समझें सीमा में दिए गए व्यंजक को निम्नलिखित रूप में लिखा जा सकता है: \[ S_n = \sum_{k=1}^{n} \frac{1}{\sqrt{2kn - k^2}} ___ ___ _______ ___ _______ _______ ___ _________.
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