100 For the infinite series S = Σ1 an, if an = (1 + )", which statement is true? S is divergent, since when OS is convergent, since when S is divergent, since when S is convergent, since when → ∞o, lim an = e. n→ ∞o, lim an = 0. → ∞, lim an = 0. n→ ∞, lim an = e.

Q: 6) (④) f Z=1 f(2)-22-132-1) sangle single 2) 렇 2Tif(20) 2Tif (2) 32-1 f(x)= /3(일) 1 = 2 . . 2Ti(2) =…

A: Here we use Cauchy integral formula which states that if f(z) is analytic inside C and z = a is…

Q: -) True or False. A series an always converges if lim,0an = 0. If true give reasen, %3D n=1 if false…

A:

Q: co s(n.n) 4- The series En=1 (n+1)2 A- Converges, B- Diverges, C- None

A: ∑n=1∞cosnπn+12 Here, an=cosnπn+12=-1nn+12 Now comparing with an=-1nbn, we get bn=1n+12 Now,…

Q: Suppose that an infinite series aj + az + az + Otherwise, the series + a, approaches a value L as n…

A: Given :  Infinite series a1 + a2 + a3 + ... + an  approaches L when n tends to ∞ .

Q: n(x+3)" Zn=1 what is the interval of convergence for the series 5" Oa. -8sx<2 O b. -8sxs2 O. -8<x<2…

A: Here we have to find the interval of convergence. Here we use Ratio test to find the interval of…

Q: Which of the following is the power series representation of - -dr? (1+x7) O a. C + Eo(-1)" 7n O b.…

A: Let given integral is

Q: Suppose x cannot = 1. Use induction on n to prove the following formula is true for all integers n…

A: We will prove the given statement.

Q: Let {an}o be a sequence with positive terms. (a) Prove that if lim van= ∞, then La, diverges. (b)…

A: According to Bartleby guidelines, I can give you a solution for only the first three subparts. so, I…

Q: Let x0, x1,x2,... be the sequence such that xo = 1 and for n ≥ 0, Xn+1 = ln(en — Xn) (as usual, the…

A: Let x0, x1, x2, ...... be the sequence such that x0=1. For n≥0, xn+1=lnexn-xn. We need to show that…

Q: Let S = Σan be a series. n=0 Which of the following statements must be true? Select all the correct…

A:

Q: Suppose {n} is a monotonically decreasing sequence of positive real numbers such that lim n = 0.…

A: Given :xnn=1∞ is monotonically decreasing sequence of positive real numberss such that limn→∞xn=0.…

Q: 10. y f(x) -2 -2+ a. f(-4) b. f(0) c. f(2) d. f(4) 4, 2.

A:

Q: 3. Prove the statement: If the series > an is convergent, then a, →0 as n→ 0. Is it also true that…

A:

Q: Which of the following infinite series converge? n(n +2) i) En=1 (n +3)³ * sin (ln n) ii) n=1 n…

A:

Q: 8. If lim a,=0, then the infinite series 2 a, must converge k=1 Select one: O True ion O False…

A: Given query is to find statement is true or false.

Q: 8. Consider the geometric series En=1 the third term az = 12. Which of the following statements…

A: Geometric series.

Q: Which one of these sequences is convergent Select one: O a. none of these. Ob. 2n+9 n' nt О с. 2n+6…

A:

Q: 4.- Suppose we have a number with infinite decimals of the form 0.d₁d₂d3d4... (where each d₂ = 0, 2,…

A:

Q: For which z's does the infinite series 1+ 좋 + + +. zn + . 3" 27 converge? To what function does it…

A: The solution are next step

Q: 1.The series E-1)" 00 converges lor all x.

A:

Q: an Suppose 2 a, and 2 bn are series with positive terms. If lim = c, where c is and value of C is…

A: We have to complete the statement

Q: For the infinite series 1 n!' antl limn 00 an Select one: a. and hence converges according to the…

A:

Q: 2. Multi-Step Series E sin(n) n2 а. b. E sin(n) n=1 n² – 5 n=1 -

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Let 2 ak converge with the positive Ak Converge with the positive term- In this case examine. the…

A:

Q: 10. Which of the following is/are correct? an is convergent. na n=1 I. For a = 2 the series II. For…

A: Option B is correct.

Q: Which of the following statements is false? 1 а. (-1)"– is a convergent series n=1 00 i 00 i+1 b.…

A: We have to check