![]() The number multiplied is called the common ratio. Geometric sequences happen when you multiply numbers. The number added is called the common difference. Note that the length of the interval is twice the radius of convergence. Sequences and Series Cheat Sheet Arithmetic Sequences and Series Geometric Sequences and Series Arithmetic sequences happen when you add numbers. ![]() Interval of convergence: I = interval of values of x for which the power series is convergent. SEQUENCES AND SERIES Since nite sums and limits are both linear, so are series. Radius of convergence: The radius is defined as the number R such that the power series converges if |x−a| R. Then- I would look up random series problems (I googled to find calc 2 finals and did the series problems there) so that you get used to all the possible tricks and so that you know how to spot which test to use. Integral Test X n0 a nwith a n 0 and a ndecreasing Z 1 f(x)dx and X n0 a nboth converge/diverge where f(n) a n. (−1)nbn, where bn is a positive and eventually decreasing sequence, then I recommend making a cheat-sheet with all the different types of series and tests and memorize them. Convergence and Divergence Tests for Series Test When to Use Conclusions Divergence Test for any series X n0 a nDiverges if lim n a n 6 0. The Sequences and Series Cheat Sheet was released by ebabor on Cheatography. If L = 1, then the test is inconclusive. Calculation Cheat Sheets These are a series of Cheat Sheets that cover most of a standard Calculation I course and some topics of a Calculation II course.Suppose that an and bn are two positive sequences, and lim an Suppose an and bn are two positive sequences, with an ≤ bn for all n > N for some number N. If an = f(n) when f(x) is a positive, continuous, eventually decreasing function, then When n is large, ln(n) 1, otherwise diverges. If bn ≤ an ≤ cn for all values of n, and lim bn = lim cn = L, then it implies that lim an = L.Īn converges to zero if and only if |an| also converges to zero. We will be interested in computing limits of sequences of partial sums.Review Sheet for Calculus 2 Sequences and SeriesĪ sequence converges if lim an exists and is finite. But have you ever asked yourself how you actually compute say \(\sin(1.1)\) or \(e^ s_k = 2\). Calculus 2 Cheat Sheet by ejj1999 via /66363/cs/16562/ Taylor Series 1/1-x 1 x x x . We will focus on the basic terminology, limits of sequences and convergence of sequences in this section. Sequences In this section we define just what we mean by sequence in a math class and give the basic notation we will use with them. Given enough time, everyone is capable of computing \(x^3-2x^2 7x 11\) if say \(x=1.1\) all operations reduce to addition/multiplication of rational numbers. Here is a list of topics in this chapter. ![]()
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