Question

Using Mathematical Induction, prove: 3n < n2

-1 for n ≥ 4

Answer 1

check for n=4:

3*4 < 4^2-1
true
so, assume it's true for n=k. Check what happens when n=k+1:
3(k+1) = 3k+3
Now, we know that 3k < k^2-1, so, since k>4,
3k+3 < k^2-1+3 = k^2+2 < k^2 + 2k + 1 - 1 = (k+1)^2 - 1
So, since P(4) and P(k)=>P(k+1), P is true for all n >= 4