1 The scries n-7 Converges if n=1 A. p> 2 В. р> 2 C. p<2 D. p<2 E. p>1 F. p= 1 O F

Q: (1) Show that the series n+1 n -1 and n3 +1 n=2 converge. Be very clear about the steps you are…

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Q: he series (-1)". n=D0 4n Converges to 4 Converges to -1/2

A: The series is alternating series.

Q: The series (n+3) converge to n=1

A: by expanding the series we can find out the sum

Q: Which of the following statements is true? O E )" converges to - 2-1 7 12 O E O"' diverges n-1 O E…

A: The geometric series 1+ar+ar2+ar3+....…

Q: E Suppose we also know that 1 > an > 0. and a converge. Then the series > converge 1-an Select one:…

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Q: Which of the following is the interval of convergence of the series 00 O a. [-1/2,1/2] O b. [-1,1]…

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Q: Both of the following series converge by comparison to En=12 3 3 and 24n² + 7 24n2 – 7 n=1 n=1…

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Q: Which of the following is the sum of the series 1 T13n2 +2n if it converges?

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Q: What are all of the values of x ,such that E-1)n+1(n)* converges? x1.2 O x<1.30 x<0,40

A: By lebnitz test we observe n^x tends to inf gives zero only when x&lt;0.

Q: It is possible to find a value for a so that the series 00 1+ n° Σ na+1 n=1 is convergent. Şelect…

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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: For which value of p the series E n(1+n²Y converges. O ps-2 O p<2 O p22 O p2-2

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Q: Which of the following is the interval of convergence of the series 1 (- O a. (-1,1) O b. (-1/2,1/2]

A: Solution of the problem as follows

Q: the series : 2 3 + 7 4 5 +... 3 Select one: a. diverges b. converges absolutely C. NOTA d. converges…

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Q: Q3) Which of the following sequences and series converge and which is diverge? 4 )ET(In (e? +)*+1…

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Q: What is the convergence range of the series E=05° x' (a) 1리 5 (f) |æ| = 1

A: To find the convergence range of the given series

Q: 9).  For which p does the series ∞     n = 1 6pn 7n converge?   please show step by step .

A: This is a question of series.

Q: The series > (2)k-1 converges. k=1 Select one: True O False

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Q: Determine whether the following series (a) Σ 3η-25 [4 Marks] n=1 (b) E (- -* [4 Marks] n=1 (c) E…

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Q: (х-1)° converge absolutely? n° For which value(s) of x will the series n=1

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Q: Show that E-2 ((In n)ª/n²) converges for -o 1. n=2

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Q: 1 1 The series Σ ( – 1)" • Σ( - ( + ) " / n n n=1 converges to ∞. converges conditionally. O…

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Q: The interval of convergence of the series E 1)"(2x-3) (n+1)2 is: Select one: [2,4] none (1,2) O…

A: Probably this is a power series, there is typing error, the term (2x-3) is free from power n.

Q: 4. Does cosnx uniformly converge in [a,b] c (0, 7)? n =1 n

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Q: 6 The series E is k=0 5k Converges to Diverges None 15 Converges to 2 이5

A: Given the series is ∑k=0∞65k Sequence will be converges if it has finite value. Sequence will…

Q: For what values of x does the series converge absolutely 1 inVn 3" 2 4"x2n n(x + 3)" nx" Σ n=0 4"(n?…

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Q: The series Σ an n=1 and Σ An n=10000 either both converge or both diverge. True False

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Q: 1. Determine whether each of the following sequences converges uniformly on [0,+∞). a. fn(x) =…

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Q: d) If Can's Converger and {b,'s diverges, Hhen fanton} Converges.

A: we argue by contradiction: suppose that an+bn converges. Since an converges by assumption, the…

Q: Q3: Which of the series and sequences converges and which diverges? 3- E=1 enz 13D1 4- an = 1+ (-1)…

A: We have to find which of the series and sequence converges or which diverges.

Q: 1 converges if The series n=1 А. р> 2 В. р> 2 C. p1 F. p=1 O E OF

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Q: If E an converges, then an/n12 converges. n=1 n=1 O True False

A: True, using Abel's test.

Q: (A) True B) False The sequence {x}to, where xn = Sn² 20" is convergent. n! :

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Q: 1 If p> 1, then the series converges. kP k=1 Select one: True False

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Q: Given that the radius of convergence of the series (5х-10)" Σ is R = 0.2, the interval of…

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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: The interval of convergence of the series E t0 (n+1)(x+3)n %3D1 is equal to: (n+2) ]- 4; -2] [-4;…

A: The interval is [-4,-2].

Q: 22. What is the radius of convergence for the series "(x+2)" , n+1 1 (B) (C) 1 3. (A) 0 (D) 1

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Q: The series (k+1)* is k=1 p°k! a) Converges absolutely b) Conditionally convergent c) Diverges d)…

A: Given : series ∑k=1∞k+1kpkk! To determine the convergence of the series and choose correct option.…

Q: Which of the following is the interval of convergence of the series 1 n3" (3z–2)" . n=1

A: We can write , ∑n=0∞3-n3x-2nn Radius of convergence of function is 1.

Q: for the p-series 1 пр n=ln 1 1 1 + + 1P 2P 3P +...+ +. 1 пр A) then it converges O C) then test…

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Q: The series (k+1)* k=1_p*k! IS a) Converges absolutely b) Conditionally convergent c) Diverges d)…

A: The given series  ∑k=1∞k+1kpkk! is ; a) Converges absolutely b) Conditionally convergent c) Diverges…

Q: The sequence {C+1 In=2)"} N=1 converges to e² O None diverges converges to le converges to e³

A: The given sequence 3n+23n+1nn=1∞ The sequence can be written as follows:…

Q: If a geometric series converges to a / (1-r) if r] r<-1

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Q: ) If the series E=1 n converges conditionally and E=1 converges absolutely, then anb, converges…

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Q: What are all values of z for which the series (2-1)" A) -1 Sa<1 converges? B) 0Sz<2 S-1 C)0SS2 D) 0…

A: To find the domain of convergence of the given series.

Q: Which of the given p-series is convergent? n=1 n 2n-0.75 n=1 1 n=1 n E n1.2 n=1 All of these Σ 5/6…

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Q: Which series below conditionally converges? (-1)*-1ek VR A) Ek=1 yo (-1)k k%3D1 k3 100 K) 2k=1…

A: From the given four series, determine which of them are conditionally convergent, that is,…

Q: (e) Suppose that the functionf is represented by the power series f (x) =1- +(-1)*. - -- +... 2 4 8.…

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Q: The series An n=1 and An n=10000 either both converge or both diverge. True False

A: Notice that ∑n=1∞an=∑n=110000an+∑n=10000∞an. And ∑n=110000an is a finite series sum which is finite…

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.