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What is the simplified form of \(\frac{(n+3)!}{(n+1)!}\)?\(\frac{(n+3)!}{(n+1)!}\) का सरल रूप क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \((n+3)(n+2)\)\((n+3)(n+2)\)
Expanding the larger factorial gives \((n+3)!=(n+3)(n+2)(n+1)!\). Dividing by \((n+1)!\) therefore leaves \((n+3)(n+2)\). Option C incorrectly includes the extra factor \((n+1)\). Exam tip: In factorial division, expand the larger factorial only up to the smaller factorial and cancel the common part.क्रमगुणित के विस्तार से \((n+3)!=(n+3)(n+2)(n+1)!\)। अतः \((n+1)!\) से भाग देने पर \(\frac{(n+3)!}{(n+1)!}=(n+3)(n+2)\) मिलता है। विकल्प C में \((n+1)\) अनावश्यक रूप से शामिल है। परीक्षा टिप: क्रमगुणितों के भाग में बड़े क्रमगुणित को छोटे क्रमगुणित तक फैलाकर समान पद काटें।
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