Lim n -n-2 -n-1 -n-2 -n-1 - is

The correct option is B 1 lim_n →∞(n + 2 ) !+ (n +1)!/(n + 2)! (n+ 1)! Dividing N' and D' by (n + 1) !: ⇒lim_n →∞(n + 2)(n+1)!/(n +1)!+1/(n+2)(n+1)!/(n+1)! 1 = ...

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Byju's Answer

Standard XII

Mathematics

Indeterminate Forms

lim n →∞n+2 !...

Question

${lim}_{n \to \infty} \frac{(n + 2)! + (n + 1)!}{(n + 2)! - (n + 1)!}$ is

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-1

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None of these

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Solution

The correct option is C
1

${lim}_{n \to \infty} \frac{(n + 2)! + (n + 1)!}{(n + 2)! - (n + 1)!}$
Dividing N' and D' by (n + 1) !:
$\Rightarrow {lim}_{n \to \infty} \frac{\frac{(n + 2) (n + 1)!}{(n + 1)!} + 1}{\frac{(n + 2) (n + 1)!}{(n + 1)!} - 1} = {lim}_{n \to \infty} \frac{n + 2 + 1}{n + 2 - 1}$
$= {lim}_{n \to \infty} \frac{n + 3}{n + 1} = {lim}_{n \to \infty} \frac{1 + \frac{3}{n}}{1 + \frac{1}{n}}$
= 1

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Similar questions

\lim_{n \to \infty} [\frac{(n + 2)! + (n + 1)!}{(n + 2)! - (n + 1)!}]

l i m n \to \infty \frac{(n + 2)! + (n + 1)!}{(n + 2)! - (n + 1)!}

is equal to

lim n \to \infty \frac{\sqrt{1} + \sqrt{2} + . . . + \sqrt{n - 1}}{n \sqrt{n}} =

Q. Evalute

lim n \to \infty (\frac{1}{\sqrt{n} \sqrt{n + 1}} + \frac{1}{\sqrt{n} \sqrt{n + 2}} + . . . . . . . \frac{1}{\sqrt{n} \sqrt{n + n}})

lim n \to \infty \frac{\sqrt{1} + \sqrt{2} + . . . . . + \sqrt{n - 1}}{n \sqrt{n}} = 0

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limn→∞(n+2)!+(n+1)!(n+2)!−(n+1)! is

The correct option is C 1 limn→∞(n+2)!+(n+1)!(n+2)!−(n+1)! Dividing N' and D' by (n + 1) !: ⇒limn→∞(n+2)(n+1)!(n+1)!+1(n+2)(n+1)!(n+1)!−1=limn→∞n+2+1n+2−1 =limn→∞n+3n+1=limn→∞1+3n1+1n = 1

${lim}_{n \to \infty} \frac{(n + 2)! + (n + 1)!}{(n + 2)! - (n + 1)!}$ is