How do you find the first five terms of the given sequence?

enter image source here

1 Answer
Apr 15, 2018

a_1=1, a_2=1/2, a_3=1/6, a_4=1/24, a_5=1/120

Explanation:

a_1=1

a_n=1/na_(n-1)

For n=2

a_2=1/2a_1=1/2(1)=1/2

For n=3

a_3=1/3a_2=1/3(1/2)=1/6

For n=4

a_4=1/4a_1=1/4(1/6)=1/24

For n=5

a_5=1/5a_4=1/5(1/24)=1/120

Note that the closed form solution to this recursive relation is

a_n=1/(n!)