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What is the simplified form of \(\frac{(n+3)!}{(n+2)!}\)?\(\frac{(n+3)!}{(n+2)!}\) का सरल रूप क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(n+3\)\(n+3\)
Using factorial expansion, \((n+3)!=(n+3)(n+2)!\). Therefore, \(\frac{(n+3)!}{(n+2)!}=n+3\), because \((n+2)!\) cancels from the numerator and denominator. \(n+2\) is a common error caused by omitting the extra factor \(n+3\). Exam tip: Expand the larger factorial only up to the smaller factorial, then cancel common factors.क्रमगुणित के विस्तार से \((n+3)!=(n+3)(n+2)!\) होता है। अतः \(\frac{(n+3)!}{(n+2)!}=n+3\), क्योंकि \((n+2)!\) अंश और हर में कट जाता है। \(n+2\) लेने की गलती तब होती है जब अतिरिक्त गुणनखंड \(n+3\) को छोड़ दिया जाता है। परीक्षा टिप: बड़े क्रमगुणित को छोटे क्रमगुणित तक फैलाकर समान पदों को काटें।
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