In this video I go over an example of a sequence that is defined by a recurrence relationship, and then use mathematical induction to prove it is increasing, bounded, thus convergent, and finally its actual

In this video I go over an example of a sequence that is defined by a recurrence relationship, and then use mathematical induction to prove it is increasing, bounded, thus convergent, and finally its actual

In this video I go over the definition of increasing and decreasing sequences, which are thus denoted as Monotonic. - summary - playlist - notes

In this video I go over the definition of increasing and decreasing sequences, which are thus denoted as Monotonic. An increasing sequence has each consecutive term bigger than the previous, while a decreasing

In this video I discuss how to graph sequences manually as well as using Desmos online graphing calculator. - summary - playlist - notes

In this video I discuss how to graph sequences manually as well as using Desmos online graphing calculator. I also go over an example on finding the values of r in r^n that are convergent and plot them

In this video I go over Theorem 3, which states that if a sequence has a limit, then plugging it into a continuous function at that limit is the same as plugging in the limit. - summary - playlist - notes

In this video I go over 4 examples on the limits of sequences and on determining if the limits exists or the sequence diverges. - summary - playlist - notes

In this video I rewrite the general squeeze theorem into its equivalent form for sequences. Essentially, if a sequence is always between two other sequences after a given set of terms, and those two sequences

In this video I rewrite the general squeeze theorem into its equivalent form for sequences. Essentially, if a sequence is always between two other sequences after a given set of terms, and those two sequences

In this video I list the main limit laws for sequences, and which are just the general limit laws since they hold for convergent sequences as well. - summary - playlist - notes

In this video I list the main limit laws for sequences, and which are just the general limit laws since they hold for convergent sequences as well. In each law, the sequence(s) are convergent, and the

In this video I go over the notation and precise definition for sequences that diverge to infinity when the number of terms go to infinity. - summary - playlist - notes

In this video I go over the notation and precise definition for sequences that diverge to infinity when the number of terms go to infinity. The precise definition states that the limit of a sequence approaches

In this video I go over a more precise definition of the limit of a sequence by using the same approach as for the limit of a function. If the limit of a sequence exists, then there must be a positive

In this video I go over a more precise definition of the limit of a sequence by using the same approach as for the limit of a function. If the limit of a sequence exists, then there must be a positive

In this video I go over a quick intro to sequences (which are ordered lists of numbers) and series (which are sums of sequences). Isaac Newton represented functions as sums of infinite series, which paved

Note: NOT numerology. Just numbers. The infinitely repeating pattern through doubling and simplifying is 1, 2, 4, 8, 7, 5, 1...(looks musical to me). Note there's no 3, 6 or 9 in the pattern 1+1 = 2 2+2