Prove that the the sequence [math] n^2[/math] diverges to infinity

The sequence is strictly increasing since [imath]\forall n \in \mathbb{N} : (n+1)^2 = n^2 + 2n + 1 > n^2 [/imath].

 

The sequence is not bounded above since [imath]\forall b \in \mathbb{R} , n>b : n^2 > b^2 \geq b[/imath].

 

And it's well known that a strictly increasing sequence is only convergent if it is bounded above.

 

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