Defining Convergent and Divergent Infinite Sequences
First up, let's talk sequences! Think of a sequence as an ordered list of numbers, a parade of terms
Series of Constants, The nth Term Test, and Harmonic Series
Alright, now for the mind-blowing part! What if we take all those numbers in a sequence and *add the
Integral Test and p-Series
Okay, so the nth Term Test is a quick check, but it's often inconclusive. What's next? Enter the **I
Comparison Tests
But what if your series isn't a p-series, and you can't easily integrate it? Don't fret! We have **C
Alternating Series Test
So far, we've mostly dealt with series where all the terms are positive. But what happens if the ter
Ratio Test and Root Test
Alright, next up are two of the most powerful tests, especially when you see factorials (like n!) or
Power Series and Radius of Convergence
Now, let's bring it all together! All these tests lead us to the magnificent world of **Power Series
Taylor and Maclaurin Series: Part 1 (Polynomial Approximation)
Why do we care so much about power series? Because they allow us to approximate complicated function