In this video I go over the history of the Fibonacci sequence and Fibonacci numbers as well as their relation to the Golden Ratio and Golden angle, rectangle, and spiral. - summary - playlist - notes #math

In this video I go over the history of the Fibonacci sequence and Fibonacci numbers as well as their relation to the Golden Ratio and Golden angle, rectangle, and spiral. Although the Fibonacci sequence

In this video I go over the first appearance of the famous Fibonacci sequence and show that the limit of the ratio of two consecutive terms is equal to the Golden Ratio. The Italian mathematician Leonardo

In this video I go over the first appearance of the famous Fibonacci sequence and show that the limit of the ratio of two consecutive terms is equal to the Golden Ratio. The Italian mathematician Leonardo

In this video I prove Theorem 3, which states that a convergent sequence with limit L can be plugged directly into a continuous function at L, thus obtaining f(L). - summary - playlist - notes #math #sequences

In this video I prove Theorem 3, which states that a convergent sequence with limit L can be plugged directly into a continuous function at L, thus obtaining f(L). I prove this using the precise definition

In this video I prove Theorem 2, which states that if the limit of the absolute values of a sequence is zero, then the sequence itself approaches zero. I solved this using both Squeeze Theorem and the

In this video I prove Theorem 2, which states that if the limit of the absolute values of a sequence is zero, then the sequence itself approaches zero. I solved this using both Squeeze Theorem and the

In this video I show that the limit of a sequence is the same if the sequence was shifted by 1 term. I use this fact to solve for the limit of a recursive sequence by plugging in the limit into the recursion

In this video I show that the limit of a sequence is the same if the sequence was shifted by 1 term. I use this fact to solve for the limit of a recursive sequence by plugging in the limit into the recursion

In this video I first go over the definition of bounded sequences, then discuss the completeness axiom in number theory and how it is used to proof the monotonic sequence theorem. - summary - playlist

In this video I first go over the definition of bounded sequences, then discuss the completeness axiom in number theory and how it is used to proof the monotonic sequence theorem. A sequence is bounded

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