Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • <img alt="\lim _{n \rightarrow \infty} \frac{a^{n}}{n !}(a>0)" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Clim%20_%7Bn%20%5Crightarrow%20%5Cinfty%7D%20%5Cfrac%7Ba%5E%7Bn%7D%7D%7Bn%20

\lim _{n \rightarrow \infty} \frac{a^{n}}{n !}(a>0)

Option: 1

is infinity


Option: 2

is 1


Option: 3

is 0


Option: 4

does not exist


Answers (1)

best_answer

 

Let K be a positive integer such that \mathrm{K} \leq \mathrm{a}<\mathrm{K}+1.

Then 0<\frac{a^{n}}{n !}<\frac{a^{k}}{K !}\left(\frac{a}{K+1}\right)^{n-k} \rightarrow 0 as \mathrm{n} \rightarrow \infty. Thus by sandwitch theorem the required limit is zero.

Posted by

rishi.raj

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Latest Question