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Learn AP®︎ Calculus BC—everything from AP®︎ Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP®︎ test.
By now, you should be familiar with several kinds of series like arithmetic or geometric series. Riemann sums are also series. This is actually a vast and fascinating world: the world series!
Some infinite series converge to a finite value. Learn how this is possible and how we can tell whether a series converges and to what value. We will also learn about Taylor and Maclaurin series, which are series that act as functions and converge to common functions like sin(x) or eˣ.
This video shows how to find a rule for the nth term (aₙ) in a series. We start with the formula for the sum of the first n terms (sₙ). Then, we subtract the sum of the first n-1 terms (sₙ₋₁) from sₙ to get aₙ. Finally, we simplify the expression.
Sequences are like chains of ordered terms. Series are sums of terms in sequences. These simple innovations uncover a world of fascinating functions and behavior.
Get ready for AP® Calculus; Get ready for AP® Statistics; Math: high school & college; Algebra 1; Geometry; Algebra 2; Integrated math 1; Integrated math 2; Integrated math 3; Algebra basics; Trigonometry; Precalculus; High school statistics; Statistics & probability; College algebra; AP®︎/College Calculus AB;
Some infinite series converge to a finite value. Learn how this is possible, how we can tell whether a series converges, and how we can explore convergence in Taylor and Maclaurin series. Skip to main content
Approximating cos(x) with a Maclaurin series (which is like a Taylor polynomial centered at x=0 with infinitely many terms). It turns out that this series is exactly the same as the function itself! Created by Sal Khan.
This unit explores geometric series, which involve multiplying by a common ratio, as well as arithmetic series, which add a common difference each time. We'll get to know summation notation, a handy way of writing out sums in a condensed form. Lastly, we'll learn the binomial theorem, a powerful tool for expanding expressions with exponents.