for n<=6 $$ 1/2 - 3/n \le0 $$ so if you are taking integer value of n, put n = 7 it gives 1/14 this is how he arrived in the conclusion ie, for $$ n\ge7 $$ $$ 1/2 - 3/n \ge1/14 $$ because n is in denominator it will only decrease the value of -ve term so overall value will increase with n ,which is the constant c1.
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