Question

the principal of mathematical induction ,prove that n^2<n!​

Answer 1

Answer:

Step 1: prove for n=1

1 < 2

Step 2:

n+1<2⋅2n

n<2⋅2n−1

n<2n+2n−1

The function 2n+2n−1 is surely higher than 2n−1 so if

n<2n is true (induction step), n<2n+2n−1 has to be true as well.