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If (S_n=1128), what will (n) be?यदि (S_n=1128), तो (n) क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 4747
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Here, \(\frac{n(n+1)}{2}=1128\), so \(n(n+1)=2256\). Since \(47\times48=2256\), \(n=47\). Option 48 is not correct because \(\frac{48\times49}{2}=1176\). Exam tip: for such questions, look for two consecutive factors whose product is twice the given sum.प्रथम n प्राकृतिक संख्याओं का योग \(S_n=\frac{n(n+1)}{2}\) होता है। यहाँ \(\frac{n(n+1)}{2}=1128\), अतः \(n(n+1)=2256\)। \(47\times48=2256\), इसलिए \(n=47\)। विकल्प 48 सही नहीं है, क्योंकि \(\frac{48\times49}{2}=1176\) होगा। परीक्षा टिप: ऐसे प्रश्नों में 1128 के पास के दो क्रमागत गुणनखंड खोजें।
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