This helps visualize a decreasing monotone sequence’s convergence, and also talks about the convergence theorem. This will help more visual learners.

http://www.sciencedirect.com.libserv-prd.bridgew.edu/science/article/pii/S0096300315009881

This source gives formal proofs about convergency of geometric and algebraic sequences.

S(N+1)=S(N)+1/(N+1)^2 Find if it is convergent.

Give examples of sequences of rational numbers {an} with an
upper limit √ 2 and lower limit − √ 2

Let α and β be positive numbers.
Discuss the convergence behavior of the sequence α βn β αn