Simplifying the 😱BIG RATIO TEST FRACTION😱 #apcalculus #apcalc #unit10 #shorts

We explore a crucial aspect of Unit 10 in AP Calculus BC: the application of the ratio test for series convergence. One of the trickiest steps in utilizing the ratio test efficiently is the simplification of a substantial absolute value, a challenge we tackle head-on.

The ratio test involves calculating L, the limit of the absolute value of the ratio of consecutive terms in a series, as n approaches infinity. We start with a series a_n and proceed to find L by examining the limit of the absolute value, where the denominator is a_n (our original series term) and the numerator is a_(n+1), which we get by replacing n with n+1 in our series formula. Our goal for simplifying the big fraction is to break it into multiple fractions and simplify those individually, recombining them all later in order to streamline the expression.

#APCalculusBC #RatioTest #ConvergenceTest #CalculusTutorial #MathEducation

Unit 10 of AP Calculus is all about Infinite Sequences and Series:
10.1 Defining Convergent and Divergent Infinite Series
10.2 Working with Geometric Series
10.3 The nth Term Test for Divergence
10.4 Integral Test for Convergence
10.5 Harmonic Series and p-Series
10.6 Comparison Tests for Convergence
10.7 Alternating Series Test for Convergence
10.8 Ratio Test for Convergence
10.9 Determining Absolute or Conditional Convergence
10.10 Alternating Series Error Bound
10.11 Finding Taylor Polynomial Approximations of Functions
10.12 Lagrange Error Bound
10.13 Radius and Interval of Convergence of Power Series
10.14 Finding Taylor or Maclaurin Series for a Function
10.15 Representing Functions as Power Series

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[Jason-mirj]

I love how you explained things so throughly, thank you, I wish I could’ve find you a week ago when I had my Cal 2 final; Still passed with a A tho 😁😁