Using Mathematical Induction to find the Limit of a Recursive Sequence https://youtu.be/BHnjY22ddOM

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 limit.

#math #sequences #mathematicalinduction #calculus #education

Plugging a Sequence into a Function and Examples

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. https://youtu.be/5Vc8QX_I7KA

#math #science #education #limits #sequences

Infinite Limits of Sequences at Infinity https://youtu.be/a4M4w3PhCd8

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.

Sequences: Definition, Notation, Fibonacci, and Examples https://youtu.be/jlDvjip0hLk

In this video I go over sequences, which are just ordered lists of numbers, the notation used to describe them, and several examples to illustrate how to obtain the general formula of the terms of a sequence. I also discuss briefly discuss the famous Fibonacci sequence, which is defined recursively by adding up the previous two terms.

Introduction to Infinite Sequences and Series https://youtu.be/dhBcdt4-N4c

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 the way for many applications in physics, chemistry, and science in general.

Cubic Formula Proof Step 5: Putting it All Together to Solve for x https://youtu.be/ZpYMkiRIbkU

In this video I go over the fifth and final step of the Cubic Formula proof which involves putting all of the previous steps together to solve for the 3 solutions of x. Because I used the copy and paste method in Microsoft OneNote, I may be the first person to show the complete solution being derived in real-time!