10. If * a, > 0 and an converges, then (-1)"a, diverges True False

Q: 5 1 3 1 1- Show that the series 2 + 24 4 1 +4 43 + + .. is convergent. - - - - 3 42

A: We can answer first question as per the honor policy. Please resubmit other question as well to know…

Q: Prove that the sequence given by 2.4. 6.(2n) Un = 3.5.7.…(2n + 1) converges and find its limit.

A: Given query is to prove that sequence converges.

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

A:

Q: 00 Show that converges if [r| < 1. п: п

A: The given series is

Q: 20. Show that if E-1a, converges, then 1 + sin(a,) Σ n=1 converges.

A:

Q: 3 Show that the (sn} sequence given in general terms converges. Sn + n+2 n+1 2n +

A:

Q: If lim bn pe 0= =1 || En=1 a, converges, then En=1 b, diverges.? True False

A:

Q: N! 9) Show that converges/diverges

A: Use D Alembert ratio test

Q: if Xn is bounded, is Xn  cauchy ?  is Xn convergent?

A: Solution

Q: State why the following intergral is improper and find the value if it is convergent: 2r (z² – 4) "

A: The given integral is I=∫262xx2-423dx The integral is improper as the integrand is unbounded at x=2.

Q: Apply the Roio Test OR diver GeNT. CONverGe NT 8. 5h

A: Given query is to find series converges or diverges using ratio test.

Q: Suppose that anx" converges for x = 5. Must it also converge for x = 4? What about x = -3?

A:

Q: If lim a, is not 0 then 2 a, is convergent n=1

A: By using theorem we can say that

Q: 3. Prove that the sequence sin(n) (0, 1). converges to n n+1

A: We calculate both limit separately as n tends to infinity.

Q: We can show that the series 1 2" – n n=1 Σ is convergent by applying the limit comparison test with…

A:

Q: 1 3 .5 4 X +x

A:

Q: 59. Show that 1- sin x dx converges. x? 00

A:

Q: Find a sequence X, such that it does not converge to any real number, but Y, does converge to some…

A: Any real sequence Xn is said to be convergent if Xn converging to a unique real number. That is, if…

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: ) Prove that if XnXnand YnYn are any two sequences of real numbers such that XnXn converges to xx…

A:

Q: What are all of the values of x ,such that Σ.. (-1)" + 1 converges? (31)"

A:

Q: 4. Show that the sequence {fn}, where nx fn(x) = xER 1+n°x is point-wise convergent but is not…

A:

Q: 2 n 1 o Show that + converges/diverges n-

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Q: S sin(n) cos(n)/n converges or 3. Use to sandwich/squeeze theorem to argue whether the sequence 1+n…

A: We need to find if series converges or diverges.

Q: etermine and justify if ∞ In(x) k=2 (1+k) ³/2 converges or diverges.

A: given series ∑k=2∞ln(x)(1+k)3/2

Q: 13. If x1 := 2 and x+1 = 2+1/x, for n 2 1, show that (x,) is a contractive sequence. What is its…

A: Given x1 = 2 xn+1 = 2 + (1/xn) We need to show that (xn) is a contractive sequence and we need to…

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

A:

Q: If 2 Cnx" is convergent when x=2 and divergent when x=-3, then 2 Cn is n=0 n =0 convergent. O…

A: Consider the given information: The series ∑n=0∞Cnxn is convergent when x=2 and divergent when x=-3.…

Q: 1 x converges 1 ex - e-X Select one: True False

A:

Q: What is the convergency interval of (2n)l

A: The given series is,  ∑n=1∞n!23n2n!xn To find its interval of convergence.

Q: show : ΣΣ - a"d, (x - a)" | n=0 m=0 is convergent,

A:

Q: The sequence (tanh n) converges to2

A:

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

A:

Q: Prove that or 「+ X。- ズー 2. 71 number J2 Converged to

A:

Q: Suppose SELECT ALL A) sometimes converges depending on the sequence, a(n) B) lim a(n) # 0 never…

A: Given that, limn→∞a(n)≠0 then we have to find ∑n=1∞a(n) is convergence or divergence or depends.

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: If conditionally converges then Jan| converges. 2=1 n=1 True False Rationale:

A:

Q: Suppose that p(x)=an" converges on (-1, 1], find the interval of convergen n=0 8 left end included…

A:

Q: (1) Show that n2 +1 n=1 converges conditionally. Show that all conditions of the test used are…

A:

Q: The sequence (Xn) = (1, 3, 1, 3, 1, . . . , 1, 3, ...) is: Converge to 3. O Divergent. Converge to 0…

A:

Q: Show that 2"x" converges if |x| <. n=1

A:

Q: 8. Suppose ar > 0 and Does > ak converge or k diverge? Why? %3D

A:

Q: Suppose that an object starts with an initial velocity of v0(in ft/sec) and moves under a constant…

A: Given,

Q: , (n!)²3"| What is the convergency interval of www (2n)! O a. (-2/3,2/3) O b. (-4/3,4/3) O c.…

A: Here we have to find the convergency interval of the given series.

Q: 4. Show that the sequence {fn}, where nx fn(x)=- xER 1+n°x' is point-wise convergent but is not…

A:

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

A:

Q: 1.4 Does (fa(r)} in 1.3 converges uniformly on |-3,3]? Explain.

A:

Q: The sequence an = n- -In+1vn +3 converges to the limit %3D A) -3 B) -1 C) 1 D) +2 E) -2

A:

Q: Find a sequence X, Such that X, does not converge (to any XE R) and Y, does converge to 0 where Y,…

A:

Q: Show that the series n" (2n)! is convergent. Deduce that lim 0. (2n)! n=1

A: