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If \(S_n=\frac{n(n+1)}{2}\) and \(S_n=861\), what is the value of (n)?यदि \(S_n=\frac{n(n+1)}{2}\) और \(S_n=861\) है, तो (n) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 4141
Given \(\frac{n(n+1)}{2}=861\), we get \(n(n+1)=1722\). Since \(41\times42=1722\), \(n=41\). For the close distractor \(40\), the sum is \(\frac{40\times41}{2}=820\), not 861. Exam tip: look for two consecutive numbers whose product equals twice the given sum.दिया है \(\frac{n(n+1)}{2}=861\)। अतः \(n(n+1)=1722\)। क्योंकि \(41\times 42=1722\), इसलिए \(n=41\)। विकल्प \(40\) लेने पर योग \(\frac{40\times41}{2}=820\) आता है, जो 861 नहीं है। परीक्षा टिप: क्रमागत दो संख्याओं का गुणनफल देखकर \(n\) और \(n+1\) पहचानें।
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