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Lim N → ∞ N ! ( N + 1 ) ! + N ! is Equal to

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प्रश्न

\[\lim_{n \to \infty} \frac{n!}{\left( n + 1 \right)! + n!}\]  is equal to

विकल्प

  • \[\frac{1}{2}\] 

  •  2 

MCQ
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उत्तर

\[\lim_{n \to \infty} \left[ \frac{n!}{\left( n + 1 \right)! + n!} \right]\]
\[ = \lim_{n \to \infty} \left[ \frac{n!}{\left( n + 1 \right) \times n! + n!} \right]\]
\[ = \lim_{n \to \infty} \left[ \frac{n!}{n!\left( n + 1 + 1 \right)} \right]\]
\[ = \lim_{n \to \infty} \left[ \frac{1}{n + 2} \right]\]
\[ = 0\] 

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अध्याय 29: Limits - Exercise 29.13 [पृष्ठ ८०]

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आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 29 Limits
Exercise 29.13 | Q 25 | पृष्ठ ८०

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