How can I prove that this sequence is monotonic?
So I'm supposed to prove that #{3^n/((2n)!)} _(n=1)^oo# is monotonic. From tinkering, I think it is indeed monotonic (decreasing), and I think I can prove it by induction. However, there's a method used by my professor that kinda looks like (I'll comment it below, the post is not permitting me to include another equation).
#a_(n+1)/a_n#
I get #3/(2n+1)# when I do that.
So I'm supposed to prove that
I get
1 Answer
Apr 13, 2018
In this case the ratio
Explanation:
Now, for
and so
Since all the
and so the sequence is monotonically decreasing.