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What is the value of S₁₂ + S₁₃ + S₁₄, where S_n is the sum of the first n natural numbers?जहाँ S_n पहली n प्राकृतिक संख्याओं का योग है, वहाँ S₁₂ + S₁₃ + S₁₄ का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 274274
Use the formula S_n = n(n + 1)/2 for the sum of the first n natural numbers. Thus S₁₂ = 12×13/2 = 78, S₁₃ = 13×14/2 = 91, and S₁₄ = 14×15/2 = 105. Their total is 78 + 91 + 105 = 274, so option A is correct. The original listed options and answer were inconsistent; they have been corrected here.पहली n प्राकृतिक संख्याओं के योग का सूत्र S_n = n(n + 1)/2 है। इसलिए S₁₂ = 12×13/2 = 78, S₁₃ = 13×14/2 = 91 और S₁₄ = 14×15/2 = 105। इनका योग 78 + 91 + 105 = 274 है। अतः विकल्प A सही है। पहले दिए गए विकल्पों में सही मान नहीं था, इसलिए उन्हें ठीक किया गया है।
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