1. mathematical induction inequalities

how do i show that the statement hold for every positive integer n using induction?

(1+ n)2 ≥ 3n + 1

2. Originally Posted by polymerase
how do i show that the statement hold for every positive integer n using induction?

(1+ n)2 ≥ 3n + 1
I assume you mean,
$(n+1)^2 \geq 3n+1$

It is true for $n=1$.
Assume it is true for $n=k$ that is,
$(k+1)^2 \geq 3k+1$

Then,
$(k+2)^2 = k^2+4k+4 = (k^2+2k+1)+(2k+2)\geq 3k+1 + 3 = 3(k+1)+1$