NoteI do not need an epsilon proofSolution6n2 17n 12 6n2 17

Note:I do not need an epsilon proof.

Solution

6n^2 +17n +12 > 6n^2 +17n + 5

=>

(2n+3)(3n+4) > (2n+5)(3n+1)

=>

(2n+3)/ (3n+1) > (2n+5)/(3n+4)

=>

Sn > Sn+1

=>
Sn is monotone.

2n < 9n

=>

2n +3 < 9n +3

=>

2n+3 < 3(3n+1)

=>

(2n+3)/(3n+1) <3

=>

sn = (2n+3)/(3n +1) < 3

=>

0 < sn <3

=>

Sn is bounded

thus proved