What is the formal proof that a sequence diverges

[transgalactic]

i got (n^2+1)/n
when n->infinity the limit is infinity.
what is the formal proof that a sequence diverges ?

 

[maks4]

I don't know the formal proof off by heart, but you could use L'Hopital's rule to see that it diverges(?).

 

[Mark44]

i got (n^2+1)/n
when n->infinity the limit is infinity.
what is the formal proof that a sequence diverges ?

Show that for any (large, positive) number M, there exists another number N for which, if n >= N, then a_n > M.

So someone gives you a number M.
You find another number N so that a_N+1, a_N+2, a_N+3, ... all are larger than M.

For your sequence, solve (n^2 + 1)/n > M for n. From that, choose a number N.

Clear?