/sci/ - Science & Math

Help with a baby tier analysis proof?

Basically, for a sequence bounded in an interval in the reals, then that sequence with an added factor of 1/n will converge to a real number.

So far I've tried to show that, since our arbitrary given sequence is bounded above and below, the limsup and liminf of that sequence are also within the interval. My hope is to show that the subsequences that approach the limsup and liminf, when having the added factor of 1/n, will clearly approach a specific real number, ie that the limsup=liminf But I'm a little lost and I don't know if this is a good approach.