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What is the simplified form of \(\frac{(n+2)!}{n!}\)?\(\frac{(n+2)!}{n!}\) का सरल रूप क्या 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 \(\frac{(n+2)!}{n!}=\frac{(n+2)(n+1)n!}{n!}=(n+2)(n+1)\). The option \(n(n+1)\) incorrectly omits the factor \(n+2\). Exam tip: expand a factorial only up to the common factorial term, then cancel it.\((n+2)!=(n+2)(n+1)n!\) होता है। अतः \(\frac{(n+2)!}{n!}=\frac{(n+2)(n+1)n!}{n!}=(n+2)(n+1)\)। विकल्प \(n(n+1)\) में \(n+2\) गुणनखंड छूट गया है। परीक्षा टिप: फैक्टोरियल को आवश्यक पदों तक फैलाकर समान फैक्टोरियल पदों को काटें।
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