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What is the simplified form of \(\frac{(n+1)!-n!}{n!}\)?\(\frac{(n+1)!-n!}{n!}\) का सरल रूप क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(n\)\(n\)
Using \((n+1)!=(n+1)n!\), the numerator becomes \((n+1)n!-n!=n![(n+1)-1]=nn!\). Hence, \(\frac{nn!}{n!}=n\), so option B is correct. The distractor \(n+1\) would result if the subtraction of \(n!\) were ignored. Exam tip: In factorial expressions, first rewrite the larger factorial as a multiple of the smaller factorial.\((n+1)!=(n+1)n!\) रखने पर अंश \((n+1)n!-n!=n![(n+1)-1]=nn!\) हो जाता है। अतः \(\frac{nn!}{n!}=n\), इसलिए विकल्प B सही है। विकल्प \(n+1\) तब मिलता यदि दूसरे पद \(n!\) को घटाया न जाता। परीक्षा टिप: फैक्टोरियल वाले व्यंजकों में पहले बड़े फैक्टोरियल को छोटे फैक्टोरियल के गुणज के रूप में लिखें।
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