Word Count : 314

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हमें यह साबित करना है कि \[ S_n = 1 + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + \dots + \frac{1}{\sqrt{n}} \geq \sqrt{2(n-1)} \] ### चरण 1: असमानता को सिद्ध करने की रणनीति हम इस असमानता को गणितीय आगमन (Mathematical Induction) द्वारा साबित करेंगे। --- ### चरण 2: आधार स्थिति (Base Case) जब \( n = 2 \), तब हमें जाँच करनी होगी कि: \[ S_2 = 1 + \frac{1}{\sqrt{2}} \geq \sqrt{2(2-1)} = \sqrt{2} \] अब, चूँकि \( 1 + \frac{1}{\sqrt{2}} ____ __________ ________ ___ ___ _______ __________ ____ ______ __________ ____.
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