5n – 1 8) Σ 7n n=1

Q: E(- 1)"+1cos?n converges conditionally n=1 Select one: True False

A: We have to find whether the given statement is true or false.

Q: ∞ 00 Suppose an>0 and a diverges. Prove that n=1 n =. an contrary suppose Σ an p=g¹ + a₂ converges,…

A: We have given that , an  > 0 Also , ∑n=1∞ an diverges. We need to show that , ∑n=1∞ an1 + an…

Q: Jlgu (-1)" +1 Σ (3x)" What are all of the values of x ,such that 00 converges? n=1 x>02 C) x>3.3 O

A: Using ratio test the condition of convergence is:…

Q: HW4 Prove the following E R° Jiverges if RE[I, o) and converges if RE[O,I) Hint: Prove |-R

A:

Q: Which of the followings are false? I. 0 (-1)" is absolutely convergent. Ln=1 n² +Inn 2n II. E (-1)…

A: we have to check each options

Q: The series 2+ Vn2 1+ Vna n: is convergent if and only if: Select one: O a. 72 a d. 35 a 4

A:

Q: 3 Jlgull What are all of the values of x ,such that (-1)" + '(2n)* converges? 00 n=1 x0.3 0

A: Using ratio test condition of convergence:…

Q: IV. Determine if the given is convergent or divergent. n Σ #2. L in? + 1)² n=1 %23

A: To find Whether the series converges or diverges.

Q: n n converges, because 0 < < 1 and an 2n + 1 2n + 1 ni an is decreasing. 2n + 1 True False

A:

Q: Σ n=1 nP +1 converges if ? O A. p> 2 O B. p22 Ocp>1 O D.p22

A:

Q: H.W: Which of the sequences {a,„} converge and which diverge: 7 1. a, = 2+ (0.1)" 2. а, n

A: A sequence &lt;an&gt; is converges if limn→∞ an is finite and exists.

Q: Deter mine if the follo wing series are convergent or divergent. S u + 8n + an? 3+ 2n + n2

A:

Q: Consider an = V4n2 + 3n – 2n for n 2 1. - (a) Determine if {an}, n=1 is convergent or divergent (b)…

A: Here, an=4n2+3n-2n, n≥1     =4n2+3n-2n4n2+3n+2n4n2+3n+2n     =4n2+3n-4n24n2+3n+2n     =3n4n2+3n+2n

Q: 2n Let an = 3n +5 Determine whether {an} is convergent. Determine whether an is convergent.

A: To determine whether the given sequence and series is convergent or not.

Q: b. b; = e* + ! 1 k

A:

Q: 3. 4. En=12 () 4,

A:

Q: Which of the followings are false? 1. E0 (-1)* m%=D1 2+irn is absolutely convergent. (-1)2. is…

A: which of the following is false

Q: Use the ratio test to determine whether a_n converges,where a_n is given in the following problems.…

A: The solution are next step

Q: If an diverges and 0 (-1)"an converges. n=1 B)>(-1)"b, converges. n=1 c) 2(-1)"bn diverges. n=1 D b,…

A:

Q: Let an > 0 and assume that an diverges. Write Sn = a1 +a2 + • ·.+ an. Prove the following…

A:

Q: Write TRUE if the statement is always correct and FALSE if otherwise. Prove your answer. (a) If an…

A: The given statement is (a) If an≥0 for all n∈ℕ, then ∑n=1∞an does not converge conditionally.…

Q: If E=1 an converges, then 5 (-3) an converges. n=5 O True O False

A: We are given two statements related to series and we have to state them as true or false.

Q: SELECT (n!)? (2n)! .()* B) is similar to G A) converges C) is similar to )" D) diverges

A: We will use Ratio Test to determine convergency

Q: 8. n2 - 1 A)E n³ + 4. n=1

A: ∑i=1∞ai is said to be CONVERGENT if the sequence of partial sum results in a finite limit value for…

Q: Which of the following statements is true? O A. Η Σα, converges then Σ al converges. O B. В. Η Σα,…

A: To select: which statement about convergence is true.

Q: cos (Tn) 2. 3: 2n n=1

A:

Q: O which of the following Is true? a)E nCat2 is divengent 4" OE nt Inn is convergent ne Inn d) is…

A:

Q: Q77 You are given the following: 2 .. 1 a) 2 + 1 + 3+ z + 5 + 3 + b) + 4* Z 1 + 7* Z n=2 which of…

A:

Q: (2n)! a"(n!)2 A) diverges if |a| 2² n-1 C) converges if |a| > 2ª

A: Here we have to find the converges or diverges of the given series.

Q: 00 Which test would you use to determine whether 2n1n converges? n=1

A: The above test is called comparison test and it can be used to determine whether the given function…

Q: 1 B) V27n2 13. n=1

A:

Q: Q(3) The sequence 4n3 3n7 + n3 2n7 (a) Converges to (b) Diverges (c) Converges to

A:

Q: (-1)h 7^ (n!)? 2? (an+3)! A)is diverget B)is absolutely convergent O is conditionally conveglat

A:

Q: Sn/2", l1/2". if n is a prime number otherwise. Let an Does Ea, converge? Give reasons for your…

A:

Q: Vn7 +n Vnº + n5 n=1

A: Let's find.

Q: IV. Determine if the given is convergent or divergent. n Σ #2. (n² + 1)2 n=1

A:

Q: A Moving to another question will save this response. Question 3 k2+k+3 By using The Divergence…

A: We have to check

Q: Does it converge or diverge? Σ 2 + 2n' n=2

A: Given series is ∑n=2∞n2+2nn

Q: Which one of the following statement is correct? I. Ef2 Tmkj02r diverges. II. E C031 – kt )k…

A:

Q: H.W: Which of the sequences {a„} converge and which diverge: 1. a, = 2+(0.1)" 2. an =|1+

A:

Q: Determine if the following converge or diverge. Explain your answer: 00 Σ) 4n+1. In=1

A:

Q: cos(na)(2n2 +n-1) 1+n3 conditionally convergent, absolutely convergent, or divergent? Justify your…

A: We have to consider the following given series

Q: T or F , prove your answer Suppose (an) is Cauchy and that for every n ∈ N, the interval (−1/n,…

A: Statement is TRUE By the ARCHIMEDEAN PROPERTY AND DEFINITION OF LIMIT.

Q: 5. E-1 ne-" n=D1

A:

Q: SELECT ALL A. what condition/s would suffice to ensure A) B) Žaln) S& a(n) S&-Ea(n) converges…

A:

Q: Which of the following statement (s) is/are TRUE? I: If lim an 0 then converges n=1 1 0 and an <e",…

A: There are many tests to determine the convergence and divergence of different types of series.  For…

Q: Q3 A) Write the first five terms of the following: - 2. {1- (-1)") (3n+2 B) Determine which of the…

A: "since you have asked multiple question,we will solve first question for you.If you want any…

Q: (-1)"(7n + 1) Does En=1 converge or diverge? (3n + 1)

A: Alternating series test: If infinite series is If any of these two conditions does not hold, then…

Q: the series : 2 3 3 5 Select one: a. converges absolutely O b. converges conditionally c. diverges d.…

A: Check the given series by limit comparision test.

Q: write down detailed e− N-proofs  i) (√n+7)/(n+5) converges.  ii) (n2−3i)/(2n3+2i) converges

A: Follow the steps.