Sequence and series calculator

• [PDF File]Review Sheet for Calculus 2 Sequences and Series

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  Alternating Series Test For series of the form P ( 1)nb n, where b n is a positive and eventually decreasing sequence, then X ( 1)nb n converges ()limb n = 0 POWER SERIES De nitions X1 n=0 c nx n OR X1 n=0 c n(x a) n Radius of convergence: The radius is de ned as the number R such that the power series converges if jx aj< R, and diverges if jx ...

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• Geometric Sequences and Series - Texas Instruments

  In this sequence (above), a is the first term, r is the common ratio and n is the number of terms in the sequence. The TI-Nspire CX CAS is capable of generating formulas given the appropriate information. Enter the expression: 1 0 n k k ar Once the calculator has produced an answer, use the Algebra menu and select the Factor command and ...

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• [PDF File]Chapter 2 Limits of Sequences

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  44 CHAPTER 2. LIMITS OF SEQUENCES Figure 2.1: s n= 1 n: 0 5 10 15 20 0 1 2 2.1.1 Sequences converging to zero. De nition We say that the sequence s n converges to 0 whenever the following hold: For all >0, there exists a real number, N, such that

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• [PDF File]Recursive Sequences - Mathematics

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  sequence fangis can be given as anC1 Df.an/ and if a is a fixed point for f.x/, then if an Da is equal to the fixed point for some k, then all successive values of an are also equal to a for k > n. MA 114 ©UK Mathematics Department. 1.1. LIMITS OF RECURSIVE SEQUENCES 5

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• [PDF File]The Farey Sequence

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  The Farey sequence (of counting fractions) has been of interest to modern math-ematicians since the 18th century. This project is an exploration of the Farey sequence and its applications. We will state and prove the properties of the Farey sequence and look at their application to clock-making and to numerical approx-imations.

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• [PDF File]SEQUENCES AND SERIES

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  SEQUENCES AND SERIES 179 In the sequence of primes 2,3,5,7,…, we find that there is no formula for the nth prime. Such sequence can only be described by verbal description. In every sequence, we should not expect that its terms will necessarily be given by a specific formula. However , we expect a theoretical scheme or a rule for generating

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• [PDF File]Geometric Sequences

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  Example 2 (Continued): Step 2: Now, to find the fifth term, substitute n =5 into the equation for the nth term. 51 5 4 1 6 3 1 6 3 6 81 2 27 a ⎛⎞− Step 3: Finally, find the 100th term in the same way as the fifth term. 100 1 5 99 99 98 1 6 3 1 6 3 23 3 2 3 a ⎛⎞− ⋅ = = Example 3: Find the common ratio, the fifth term and the nth term of the geometric sequence. (a) −−

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• [PDF File]Sequences/Series Test Practice Date Period

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  ©x OKduet7ak pSXoAfStVw1aXreev pLjLGCM.3 s KAhlTl7 0rKiDgmhWtIs n RrlemseeyrfvheEdp.B o XM7agdZeb Ow2iQt2hJ CIQnpfLi0nEivtpeV sA2l7gxeZbMrnaJ b2C.Q-3-Worksheet by Kuta Software LLC Answers to Sequences/Series Test Practice (ID: 1)

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• [PDF File]Series Formulas

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  Series Formulas 1. Arithmetic and Geometric Series Definitions: First term: a 1 Nth term: a n Number of terms in the series: n Sum of the first n terms: S n Difference between successive terms: d Common ratio: q Sum to infinity: S Arithmetic Series Formulas: a a n dn = + −1 (1) 1 1 2 i i i a a a − + + = 1 2 n n a a S n + = ⋅ 2 11 ( ) n 2 ...

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• [PDF File]Sequences and Series

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  assume that each of the series considered in this section are positive term series. Most of the tests are based on the following relatively straightforward consequence of the lemma about the convergence of monotone sequences. Lemma 5. A positive term series is convergent if and only if its sequence of partial sums is bounded.

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• [PDF File]EP-Program - Strisuksa School - Roi-et Math : Sequences ...

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  2. Sequences and Series A list of number is a sequence or progression.. A sequence can be written as u u u 1 2 3, , , The nth term of the sequence is u n. 2.1 Arithmetic Sequences If the differences between successive term of a sequence are constant, then the sequence is an arithmetic progression (AP).The difference is called the common ...

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• [PDF File]MATH 1020 WORKSHEET 11.1 Sequences

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  Series A series is an infinite sum of terms. In this section we have 3 methods to determine con-vergence or divergence of series: 1) Sequence of Partial Sums and telescoping series, 2) Geometric Series, and 3) Divergence Test or nth term test. Find the sum of the convergent series X∞ n=1 1 n(n+1) Solution. Using Partial Fraction ...

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• [PDF File]SEQUENCES & SERIES LEARNING PACKET (1)

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  C. GEOMETRIC SERIES 1. The sum of the first n terms of a geometric sequence can be found using the formula: r a r S n n 1 1 1 2. Use the formula to find S 14 for {3, 21, 147…} _____ D. SIGMA NOTATION

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• [PDF File]TI-Nspire Introduction to Sequences

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  3. The sequence 4, 11, 32, can be generated by starting with 4, then multiplying the previous term by 3 and adding 1. This is done on the calculator as shown: ‘Ans’ is obtained by pressing /v. 4. The sequence 5, 6, 13, 118, … can be generated by starting with 5. Subsequent terms are generated using the ‘formula’: Ans2 – 4Ans + 1.

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• [PDF File]Sequences and summations

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  Definition: A sequence is a function from a subset of the set of integers (typically the set {0,1,2,...} or the set {1,2,3,...} to a set S. We use the notation an to denote the image of the integer n. ... • Infinite geometric series can be computed in the closed form

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• [PDF File]Math 31B: Sequences and Series

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  bigger huge positive integer. The sequence diverges to 1. 4.Plugging in a big enough positive integer into the formula a n= 1 2n will force a rubbish calculator to return 0. The sequence converges to 0. There is a formal de nition of what it means for a sequence (a n) to converge to a number L. We can visualize a sequence (a n)1 n=1 on a graph ...

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• [PDF File]Calculus BC and BCD Drill on Sequences and Series!!!

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  Geometric series are of the form: ∑a(r)n A geometric series only converges if r is between -1 and 1 The sum of a convergent geometric series is: r the first term − ⋅ ⋅ 1 See the next slide for a possible answer as to why these series are called “geometric”

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• [PDF File]Chapter 5

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  Sequences and Series of Functions 5.3. Cauchy condition for uniform convergence The Cauchy condition in Definition 1.9 provides a necessary and sufficient condi-tion for a sequence of real numbers to converge. There is an analogous uniform Cauchy condition that provides a necessary and sufficient condition for a sequence

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• [PDF File]Sequence: a list of numbers in a specific order.

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  VII. Arithmetic Series • A series is the expression for the sum of the terms of a sequence, not just “what is the next term?” Ex: 6, 9, 12, 15, 18 . . . This is a list of the numbers in the pattern an not a sum. It is a sequence. Note it goes on forever, so we say it is an infinite sequence. Ex: 6 + 9 + 12 + 15 + 18

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