Question

Use induction to prove.

Answer 1

well, whats our basis step?

Answer 2

P(4)
4^2 <= 4!
16 <= 24

Answer 3

just an idea, dunno how correct it is ......

let n=k and assume:

k^2 <= k! show that

(k+1)^2 <= (k+1)!

(k+1) (k+1) <= (k+1) * k!

(k+1) <= k!

if we can show that (k+1) < k^2 then we should be good.

Answer 4

k+1 < k^2

0 < k^2 -k -1

k > [1 +- sqrt(5)] /2

so this is true when k is at least k >= 1.62 .... which is well below our 4

Answer 5

dunno how well this proofs out tho, just an idea

Answer 6

Makes sense. It is so hard to learn this on your own

Answer 7

im glad it makes sense, just not sure if it fits the bill for induction. i cant see why not tho

Answer 8

I think your approach is right because it matches a lot of what the solution of that problem shows. I just don't understand the explanation they give