Question

Using mathematical induction, show that 3
n < (n + 2)! for all integers n ≥ 2.

Answer 1

first take n=1

Answer 2

first put n=1
int the given equation
1< (1+2)!
1< 3!
so it is correct

Answer 3

now put k
at the place of n

Answer 4

thn consider that it is true for n
and go for n+1

Answer 5

3(n+1)<(n+1+2)

Answer 6

k< (k+2)!
okay
now put k+1 = n
okay

Answer 7

I am having trouble simplfying both sides. Other induction questions were so easy but I really dont understand with this one...

Answer 8

but in the text of this exercise have wrote that n>= 2

then why begin with n=1 ???

Answer 9

@gorv !!!