Verify, using the definition of convergence of a sequence, that the following sequences converge to the proposed limit

I have a question about this solution.

I know that let N = 1/root(6e)

and n > N so n > 1/root(6e)

and make e > 1/6n^2
since 1/6n^2 is greater than original equation 1/(6n^2 + 1 )

it must be true that 1/(6n^2 + 1 ) < e I got this but from solution . n > N_{e} absolute value of (( 1/6n^2 + 4 )-0)

the last part makes me confused .

is N_{e} * absolute value of (( 1/6n^2 + 4 )-0) ?

or they just did not put comma beteewn N_{e} and absolute value of (( 1/6n^2 + 4 )-0).

so I mean the inequality should be like n> N_{e} , absolute value of (( 1/6n^2 + 4 )-0)< e =================      Yes, it may be a printing mistake. – Hardey Pandya Oct 21 at 4:09 ================= =================