Thread: limit proof

Let (x sub n) and (y sub n) be sequences of positive numbers such that
lim(x sub n/y sub n) = 0. Prove if lim(x sub n)= positive infinity, then
lim(y sub n) = positive infinity.

Originally Posted by hayter221

Let (x sub n) and (y sub n) be sequences of positive numbers such that
lim(x sub n/y sub n) = 0. Prove if lim(x sub n)= positive infinity, then
lim(y sub n) = positive infinity.

the conditions on the terms of the sequences and:



means that for all positive eventually



so:



and as goes to so must .

Now make this argument more formal and fill in the detail

CB