Calculus- +2math book

Question

If a_n = 1000*n /n!, for n = 1, 2, 3, ...., then the sequence {a_n }
(a) doesn't have a maximum
(b) attains maximum at exactly one value of n
(c) attains maximum at exactly two values of n
(d) attains maximum for infinitely many values of n

Answer 1

$a_{n} = 1000*n / n!$

$a_{1} = 1000$

$a_{2} = 1000$

$a_{3} = 500$

$a_{4} = 166.66$

$a_{5} = 41.66$

As we can see that on increasing the value of $n$ , the value $a_{n}$ except for $n = 1$ and $n = 2$  

So at $n = 1$ and $n = 2$, we are getting maximum value.

Therefore, the sequence attains the maximum at exactly two values of $n$.