4. For the sequences L (X1, X2, x3) = (50, 40, 10) %3D and (y1, y2. y3) = (3, 1,5) %3D 3 The max of yi i-1 200 240 220 None of all 380 400

Q: 8n2 + 1n + 1 an 7n2 + 9n + 9

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Q: Let {rn} and {Yn} be two sequences defined by In+1 = 2 2 xn - 1, and Yn+1 = 2xn + 6, for each…

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Q: Compute the summation. 5 > (k + 3) = | k = 1

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Q: 5. Calculate the sum of the first 23 terms of the sequence defined below. tn 10+ 3n, n E N

A: We have to find the sum

Q: Define a sequence (Sn)n inductively by letting S1 = 1, and Sn+1 = Sn + 1. 1+V5 Prove that lim Sn = .…

A: Limit of a sn

Q: 19 17- -(9n+1) (9n

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Q: The terms of a sequence of partial sums are defined by S, = Ek?, for n = 1, 2, 3, .... Evaluate the…

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Q: Find the sequence of partial sums S,, S, Sa, Sa, and Sg. 3' 00 (-1)" + 1 1 1. =1- + - .... n! 2 6 24…

A: The partial sum of a sequence S ₙ is the sum of  the first n terms of the sequence.

Q: Compute the partial sums S2, S4, and S6 of ... 2-3 3.4 4.5 5. 6 (Use symbolic notation and fractions…

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Q: 2. Find the fif th termof the + Ap-2 sequence. an=nan-l foR defined by, a, =2 ag=ろ a 152 6) 162 O172…

A: Given, a1 = -2 a2 = 3  an = nan-1 +an-2                 for         n≥3 We have to find the fifth…

Q: 1 The sequence l(n + 4) (n+ 4) diverges Select one: 20 True False

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Q: Find the first six partial sums Sı, S2, S3, S4, S5, S6 of the sequence whose nth term is given 3, 6,…

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Q: 7) Show that if a, > 0, and Lim na, 0, then the series а, + a, + а, + a, + ... diverges.,

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Q: Suppose that ho, hị, h2, . is a sequence defined as follows: ho = 1, h1 = 2, h2 = 3, %3D hy =…

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Q: 4. The same strategy from the previous page can be used to find specific entries. Given the function…

A: Generalize the terms in the sequence and find the elements  asked.

Q: 2. Find the closed form for the generation function for the sequences (i) 2, -2, 2, -2, 2, -2, - - -…

A: The closed form for the generation function for a sequence is used to define the general term of a…

Q: Let {u,} and {v,} be two sequences defined by u = (2^ – 4n + 3)/2 and v, = (2" + 4n - 3)/2 , for %D…

A: To determine the sequence wn, subtract the sequence vn from the sequence un.…

Q: Find the limit (as n → ∞) of the sequence an = In(2n² + 5) – In(5n² + 2), n > 1. %3D

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Q: 3 4 N + 1 5) Show that the sequence 7 2N + 1 is bounded and monotonic.

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Q: Compute the partial sums S2, S4, and S6 of 1 1 + • 6 1 1 + 8 · 10 + + 2. 6 · 8 (Use symbolic…

A: The given series,    12.4+14.6+16.8+18.10+......

Q: Find the limit of the sequence: 5n2 + 6n + 7 an 8n2 + 9n + 8

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Q: Let Xn, Yn be any two sequences. If XnL, YnM, then Xn YnL M

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Q: The limit of the sequence Zn = Arg(-i + ) is equal to Select one: C. 2 -3T d. 2

A: See the solution in the given fig.

Q: k

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Q: Match the sequence with the given nth term with its graph. 10n an n + 1 an an 10 10 8. 8. 4. 2 4 6 8…

A: here given  an = 10n/(n+1) for plotting put point 1,2,3,4...... first wwe put 1 a1= 10(1)/(1+1) = 5…

Q: Obtain the DFT of the given sequences using Direct method x(n) = {4,1,1,2}

A: Introduction: The discrete Fourier transformation is used to transform a discrete signal. Discrete…

Q: You may assume that 1, 1, 2, 3, 5, 8, ... has generating function 1-x – 2² (because it does). Use…

A: In the problem, it has been given that 1,1,2,3,5,.... has a generating function 1(1-x-x2) When we…

Q: 4. Prove or disprove by giving a counterexample: (a) If (xn) and (Yn) are divergent sequences then…

A: A sequence is always convergent if it's limit is unique real number. A sequence is divergent if it…

Q: 8. Suppose that họ, h1, h2, . . . is a sequence défihed as follows: ho = 1, h = 2, h2 = 3, h =…

A: I have given the proof in details

Q: Compute the partial sums S2, S4, and S6 of 1 1 + 5.6 6.7 (Use symbolic notation and fractions where…

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Q: 2. Find a formula for the sequence given by In+1 = 4xn – 5xn-1+ 2xn-2 n > 2, 5xn-1+ 2xn-2 n> 2, with…

A: We have  xn+1=4xn-5xn-1+2xn-2   n≥2    ...(i)x0=2,x1=7  and x2=15characteristic equation of (i) is…

Q: 2. Suppose x,, X2 , X3 ..... Isa sequence defined by x, = 2, X2 = 4, bk-2 + 2bk-1 for all integers k…

A: Since you have asked multiple questions, we will solve the first question for you. Note:- In…

Q: Show directly from definitions that if sn and tn are sequences so that limn→∞sn = 5 and limn→∞tn =…

A: We have two sequences sn and tn such that limn→∞ sn=5 and limn→∞ tn=∞. We have to show that limn→∞…

Q: Define a sequence (Sn)n inductively by letting S1 = 1, and Sn+1 = Sn + 1. 1+V5 Prove that lim S, = 2…

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Q: By redefining the ranges of the summations appearing on the left-hand side, show that En(n –…

A: Consider the left hand side Substitute n = n+2 in first summation, thus it becomes By…

Q: Suppose that the sequence xo, x1, X2... is defined by xo = 5, x1 = 5, and xk+2 = 16xk for k20. Find…

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Q: 4, sequence and the term in the sequence: 3 Complete the following tables if there is a relationship…

A: Hi, Thanks for posting the question. As per our guide lines, if there are more than one question, we…

Q: Suppose young Gauss had been asked to compute the sum 6 + 12 + 18 + 24 + ... + 1,494 + 1,500 1. How…

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Q: Suppose that an = 5 and b, =1 and a =7 and b, = -9, find the sum of the series: n=1 n=1 A. (-5a, +…

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Q: п+1 2n +1 dn + Vn² · 6n+1. 2n ||

A: Note some standard results of limit: limn→∞ 1+1nn=e limn→∞ n1n=1 Suppose xn and yn are two…

Q: Suppose that the sequence xo, X1, X2... is defined by xo = 0, x1 = 4, and xk+2=3xk+1+10xx for k20.…

A: Solution: Since x(k+2) is a linear combination of x(k+1) and xk, first consider solutions of the…

Q: 1. If s, = v2 and sn+1 = NOTE: To show that a sequence converges we must show that is it monotone…

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Q: Compute the summation. 5 E (k + 3) = k = 1

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Q: 7. Find the limit of the following sequences, if it exists: w {} n10 (a) +5 n! n! (Ъ) 15n2 + 1 ´…

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Q: Match the sequence with the given nth term with its graph. 10n %3D n + 1 10 2- 8 4. 主十 2 4 6 8 10…

A: topic - sequence and series

Q: 2- Suppose that (xn) is a sequence such that xn > 0 for all NE N. 1 lim n 0 Xn Show that; Xn → 0 as…

A: I have proved using Apsilon delta definition

Q: Let {Sn} n=1 to infinity, be an unbounded sequence of negative numbers. Show {Sn} n=1 to infinity,…

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Q: 6- If x(n) = {2 1-1 0 3}, h(n) = {1 2 -1) %3D %3D Find out convolution of two sequences given above.

A: Given two sequences are: xn=2,1,−1,0,3,hn=1,2,−1Find the convolution of two sequence

Q: 4 k· 2k k=1

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Q: If the terms of one sequence appearin another sequence in their given order, we call the first…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.