The sequence Converges to e Diverges Converges to 0 Converges to 2e Converges to 1

Q: Consider the sequence n²x(1 – nx) x € [0, 1/n] { - fn(x) := elsewhere . Does it converge uniformly…

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Q: solve for the valve of IL that makkes the series converge nk

A: The given series is: ∑n=1∞7nnk Let, an=7nnk;n≥1

Q: Using Sandwich Theorem, the sequence 2 = 4 – - Cos2 n +1 n³ converges to 4 converges to 2 diverges…

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Q: The sequence {( an+2 )"}1 n=1 O diverges converges to Je3 converges to e None converges to Je?

A: the given sequence converges to

Q: Find an upper bound for the error in using the sum of the first 8 terms to approximate the sum of…

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Q: 8. Determine by the ratio test if 2n=1 (2n)! converges or diverges.

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Q: * Show that the sequence (xn)n>1 in R, where In = 1- Vn' converges to 1.

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Q: Show that the error (L – s„) obtained by replacing a convergent geometric series with one of its…

A: We know that, if |r|<1, the geometric series, a+ar+ar2 + … + arn-1 + …. would converge to a/(1-r)…

Q: The sequence (n+(-1)" n Diverges Converges to 0 Converges to 1 Converges to e Converges to 2e

A: Option 3 is correct.

Q: Prove the absolute value of this series converges.

A: Given series :

Q: The sequence {()} Sn+3 Sn+1 n-1 converges to e converges fo te ConvCrges fe Ve Converges 00 Diverges

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Q: the root test fails to determine if the series (1+) n=1 converges or diverges Select one: O True…

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Q: Suppose that the power series Сn (2а — 3)" n=0 converges when x = 5.5 but not when x = -5.5. If its…

A: see below the answer

Q: Suppose that the power series (2x-5)" converges conditionally when x = 5.5. What is its radius of…

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Q: Σ Show that n2 + 1 converges/diverges n

A: The given series is: ∑n=1∞nn2+1 Let  an=nn2+1,n≥1    =nn21+1n2   =1n1+1n2 And, bn=1n

Q: If the infinite sum 7 k=2 k2 converges, use the Remainder Estimate to find lower and upper estimates…

A: Given ∑K=2∞1K72

Q: The sequence {5},-1s: 00 n=1 Converges to 5 O Converges to O Diverges. O Converges to 10 15

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Q: Q9:S a)converges to 2 b)converges to 을 c)converges to - 2 d)diverges

A: Since  you have posted a multiple  question according to guildlines I will solve first  (Q9)…

Q: The sequence a, = sin (A) is unbounded (C) converges to a number less than 1 (E) diverges to…

A: Limit of a sequence

Q: Show that the series n' (2n)! is convergent. Deduce that lim (2n)! n=1

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Q: The sequence {(1 + 1)^² +1} 2n O O converges to e² is divergent ez converges to e 2 O converges to e

A: Sequence

Q: Vn +1- n –1 n=1

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Q: What are all of the values of x, such that converges?

A: We have to use GP sum Common Ratio.

Q: Find the smallest positive integer n so that S, approximates the sum of the convergent ser to four…

A: Here we have to find the smallest positive integer n so so the Sn, approximates the sum of the…

Q: The series 2(- 1)"+1 converges n = 1 Select one: True

A: The given series is ∑n=1∞-1n+1

Q: . Use the inegral test to show that =1 converges. 1+n2

A: To solve this question first we check derivative of function is negative for n>0 and then we show…

Q: The sequence {G 3n+2 n=1 O None converges to e O diverges converges to Ve? converges to e3

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Q: A) diverges B) converges

A: If the limit exists and is a finite number, we say the improper integral converges . If the limit is…

Q: If Eanx" converges on the interval [- 7,7], where does the series Zan (2x - 5)" converge?

A: It is given that, ∑anxn converges on the interval -7,7

Q: The sequence {x}=0, where xn (A) True (B) False 20 = is convergent. n!

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Q: Find the values of the convergent series   [From n=3 to infinity] E(-1/3)^3n *that E is the sum…

A: The series can be expressed as follows.

Q: The series 3 k 1 3. is 3. convergent to O None divergent convergent to 3 convergent to

A: We have to solve

Q: Suppose that the series a,(x – 1)" converges for r = 3 and diverges for x = -4. (a) Does this power…

A: Given that ∑n=0∞an(x-1)n  The series converges for x=3. The series diverges for x=-4. (a) At x=0,…

Q: the root test fails to determine if the series Σ (1 + n= 1 converges or diverges

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Q: Use the Integral Test to show that the series Σε. n=0 converges.

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Q: The series 2n +2 Diverges to-o0 Converges to 1- Converges to B Diverges to +

A: Given series is ∑n=1∞sinπ2n-sinπ2n+2 The Nth partial sum of given series is…

Q: The series 4k O a. converges to 2 O b. diverges to oo O C. converges to 4 O d. converges to = O e.…

A: We have to check the Converges

Q: The sequence {G1)}m1 5n+3 5n+1 n=1 Diverges converges to Je3 converges to Je² converges to 0…

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Q: 1dx x²+2x+5 -00 O diverges O None 37 converges to 4 converges to converges to converges to 3r

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Q: Use comparison test to show that the series E=1 (2) converges. 5n2-п.

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Q: The series is k=0 convergent to 3 divergent 5 convergent to 2 O None convergent to

A: To check whether the given series is convergent or divergent

Q: The series C, (x + 6)" converges at x = -3 and diverges at x = -12. Based on this information, what…

A: Given series: ∑Cnx+6n converges at x=-3 and diverges at x=-12

Q: 2. Use the previous item to determine if the improper integ 2x – x3 d.x (x – 1)²(x² +1) 8∞ converges…

A: This is a problem of improper differential equation. First by partial fraction decomposition we will…

Q: Find the rate of convergence of the sequence {(- 2 sin as n n=1 .n → o(:)° 1 n 1 n2 n3

A: Here we will find the rate of convergence,

Q: Consider the sequence defined by xo = a > 0 and %3D a X+1 = } ( x* + -) Xk Prove that this sequence…

A: Rate of convergence: Assume we have a series of real numbers that all converge to x. x0, x1, x2,...,…

Q: The improper integral | 1 x²+2x+5 1 O None O diverges converges to 8 converges to 37 4 O converges…

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Q: 1. Show that the sequence ((nx - - 1/n)e n) converges uniformly on [0, 0). (15 points)

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Q: 2" Зп+2 n=0

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Q: 5. Show that the sequence Pn = 1 converges linearly to p 0, and the sequence Pn = 10-2" converges…

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.