June 26, 2019
The limit, if it exists, is unique.
If a sequence, an, has a limit, all the subsequences have the same limit as an.
There are bounded sequences that are not convergent.
All the monotone and bounded sequences are convergent.
There are convergent sequences that are not monotonous.
Rules of Limits
lim (an + bn) = lim (an) + lim (bn)
lim (an − bn) = lim (an) − lim (bn)
lim (an · bn) = lim (an) · lim (bn)
lim (an : bn) = lim (an) : lim (bn)
lim k · an =k · lim an
lim ank = (lim an)k
lim loga an = loga lim an
By applying these rules, the following cases are presented: