Demonstrate that the limit from these successions is 0 using the definition

[the ninsk]

Hello, I am not sure how to find an expression that leaves n>(an expression with epsilon in the denominator).
Would this be correct?
Thanks

 

[Steven G]

How do you go from n^2<e to n^2>1/e??

Let n^2=1/2 and e = 6/10.

Then surely 1/2 = .5 < 6/10=.6

However, 1/2 >1/.6?? Since 1/.6 >1, then surely 1/2 < 1/.6


From another angle. Since e>0 can be any value (especially as small as we like), then at some point n^2<1/e, since 1/e -->oo as e-->0.