1.

The limit, if it exists, is unique.

2.

If a sequence, an, has a limit, all the subsequences have the same limit as an.

3.

All convergent sequences are bounded.

4.

There are bounded sequences that are not convergent.

5.

All the monotone and bounded sequences are convergent.

6.

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:

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.