Question

Show through induction that the SEQUENCE diverges:

Answer 1

\[\frac{ 1*3*5......(2n-1) }{ n! }\]

Answer 2

Induction wasn't covered in class, but this is hw so.....

Answer 3

Okay, I think I should start off by saying that I don't know how to do anything through induction. So if what was just posted was some induction procedure, I'm sure what needs to be done. This is something that kind of needs to be introduced like I'm dumb to it. Is there a procedure for induction or is it just some fancy name for something or....? And to be honest, not sure I even understood the explaantion x_x

Answer 4

*not sure

Answer 5

eashy is so wrong here. He's only really done part of it, there are two things to do for induction:

Show that it's true for the base case, so in this case n=1. 1 isn't infinity, so this converges so far. For instance, the sum of 1/n^2 converges, and its base case is 1 as well.

Answer 6

Okay, but what kamui said then makes me question that process. FInd a f(n) that satisfies the condition. But if you chose f(1), clearly n = 1 is going to just give you a finite answer
\[\frac{ 2(1)-1 }{ (1)! }= 1\]

Answer 7

Okay, made a massive mistake that may change things x_X Was supposed to be sequence, not series.....

Answer 8

this makes a lot more sense now

Answer 9

actually i have no idea how to prove this using induction. the following proof works, but isn't really based on induction

t(n+1)=(2n+1)/(n+1) * t(n).
as n->infinity, t(n+1)=2*t(n)
therefore the sequence approaches infinity, since the term ratio is greater than 1.