Can you explain what is in red in the following figure? Thank you

Show that for any real constants a and b, where b > 0, (n + a)"- (nb) To prove this, we have to show that there exists constants c1,C2,no>0 such that 0 no. Note that, n-a 2?a?, As b0, we can raise all the terms of the previous inequality to the power of b without breaking the inequality s((n+a s (2n) So, (n +a)(n) because there exists c1/2, 2, and no 2a