$lim n \to \infty \frac{(n + 2)! + (n + 1)!}{(n + 3)!} =$

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{1}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $0$
We divide the numerator and the denominator by $(n + 3)!$
The expression is,
$= {lim}_{n \to \infty} \frac{(n + 2)!}{(n + 3)!} + {lim}_{n \to \infty} \frac{(n + 1)!}{(n + 3)!}$
$= {lim}_{n \to \infty} \frac{(n + 2)!}{(n + 3) (n + 2)!} + {lim}_{n \to \infty} \frac{(n + 1)!}{(n + 3) (n + 2) (n + 1)!}$
$= {lim}_{n \to \infty} \frac{1}{(n + 3)} + {lim}_{n \to \infty} \frac{1}{(n + 3) (n + 2)}$
$= 0 + 0 = 0$
Hence, option 'C' is correct.

Suggest Corrections

Similar questions

lim n \to \infty \frac{(n + 2)! + (n + 1)!}{(n + 2)! - (n + 1)!} =

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

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

lim n \to \infty \frac{1}{(n + 1)} + \frac{1}{(n + 2)} + \frac{1}{(n + 3)} + . . . + . . . \frac{1}{(n + n)} = ?

n \in N

Δ_{n} = ∣ ∣ ∣ ∣ ∣ \begin{matrix} n! & (n + 1)! & (n + 2)! (n + 1)! & (n + 2)! & (n + 3)! (n + 2)! & (n + 3)! & (n + 4)! \end{matrix} ∣ ∣ ∣ ∣ ∣

lim n \to \infty \frac{(3 n^{3} - 5) Δ_{n}}{Δ_{n + 1}}

Join BYJU'S Learning Program