I don't quite understand the problem presented, so please correct me if I do not. I will try to answer your question nonetheless.
I'm assuming I have to use mathematical induction to prove the question, but I'm confused about the sequence. For that reason, I'm going to assume it's
But it could also be
Or maybe I lack knowledge of this subject. I will still hold my stance that this is an induction problem, therefore the first step can be complete regardless of the sequence.
If even that statement is false, please ignore this answer and call on someone more capable to write one for you. If I am headed in the right path, please continue.
First, we need to complete the base case. Substitute
#(1) = (2(1)!)/(1)!#
#1 = 2/1#
#1 cancel(=) 2#
This is not true
Assuming my method was correct or at least sufficient enough to complete the base case, the question is false. Since
Again, please inform me on whether or not I answered your question at all.