So far in this course you have seen several sequences that converge with proofs of their convergence. These include:
We want to build up our repertoire of such sequences, and we start by looking at addition.
Theorem.
Proof.
Subproof.
So
This result enables us to write down the limit of sequences such as
1+
Proposition.
Let (
Proof.
These two results show a similar theorem also holds for subtraction.
Theorem.
Proof.