We prove that the arithmetic averages of a convergent sequence converges to the same limit. This result introduces us to a very basic trick in analysis, namely, Divide and Conquer. We also deal with monotone sequences and apply the results to the decimal expansion.
00:00 Start
00:50 Review of earlier results
09:45 Sequences of arithmetic means of a convergent sequence converges to the limit of the original sequence
33:40 Monotone sequences
41:00 Monotone convergence theorem
54:25 Some examples of monotone sequences
59:25 Replacing finitely many terms of a convergent sequence does not affect the convergence and the limit
1:03:03 Decimal expansions
