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Which is the correct simplified form of \(\frac{(n+2)!}{n!}\)?\(\frac{(n+2)!}{n!}\) का सही सरल रूप कौन सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \((n+2)(n+1)\)\((n+2)(n+1)\)
Since \((n+2)!=(n+2)(n+1)n!\), we get \(\frac{(n+2)!}{n!}=\frac{(n+2)(n+1)n!}{n!}=(n+2)(n+1)\). Therefore, option C is correct. \(n+2\) is only one factor and misses the factor \((n+1)\). Exam tip: In a factorial ratio, expand the larger factorial up to the smaller one and then cancel common factors.क्योंकि \((n+2)!=(n+2)(n+1)n!\), इसलिए \(\frac{(n+2)!}{n!}=\frac{(n+2)(n+1)n!}{n!}=(n+2)(n+1)\)। अतः विकल्प C सही है। \(n+2\) केवल एक गुणनखंड है; इसमें \((n+1)\) गुणनखंड छूट जाता है। परीक्षा टिप: फैक्टोरियल के अनुपात में बड़े फैक्टोरियल को छोटे फैक्टोरियल तक फैलाकर लिखें, फिर समान पदों को काटें।
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