Q: (b) Let a1 = 1 and an+1 = lim, an- /am+2. Prove that a, is convergent and find %3D
A: The recursive relation represent a bounded above increasing sequence
Q: T F If {an} is convergent, then {|an|} is convergent.
A:
Q: 1 En=1 4n² 8n +3
A: ∑n=1+∞ 14n2-8n+3using limit comparison testlimn→∞ 14n2-8n+31n2limn→∞ n24n2-8n+3factorisinglimn→∞…
Q: 2 sin x+1 dr 3 -dx +1
A:
Q: sin(n) Q2: Does En=2 convergent or divergent by use integral test? n2
A: Explanation of the answer is as follows
Q: 3. Use the Test for Divergence to explain why if En-0 an converges, then En=0 am must diverge.
A:
Q: 1+e-* Show that dr diverges.
A:
Q: 3 1+e п
A:
Q: QDTest for convergent and divergent : (show your work) e-2 1. ΣΟ-1 n+cos²n
A: answer : this is divergent
Q: Enter its finite) value if its 5. a) I5 the generalised integral convergent or divergent?…
A:
Q: exmine if HS Convergent or divergent a) 2n²+3 8n7 7ntG
A:
Q: sin (nx + 3) f (x) = is convergent point wise to zero function. %3D n – 1 ylgn O İhi
A:
Q: /2n?
A: The given series is: ∑n=1∞(-1)n(-1)n2n2+5=∑n=1∞(-1)2nn2+5n2=∑n=1∞1n2+5n2
Q: -2x Determine whether |e*dx is convergent or divergent. If it is convergent state what value the…
A: Given ∫0∞e-2xdx
Q: Determine whether it converges or diverges. You must provide justification for your answer. sin(æ')…
A:
Q: Sequences {xn} and {yn} such that they are both convergent and {xn+yn} maps to 5
A:
Q: • If it converges, what is its limit? Provide some justification for your answer. • If it diverges,…
A: key points By monotone convergence theorem ; if a sequence is decreasing and is bounded below by an…
Q: If lim =c>0 , then b, , a, both convergent and both divergent.
A: By limit ratio test we know that if above condition is true then either both series diverges and…
Q: Determine convergence or divergence using any method covered so f 5" +10" 17" DA. convergent DB.…
A: See the details solution in below
Q: Σ n=1 (2n+ 1)3/2 Use the Integral Test to determine if converges or diverge:
A:
Q: sin In(n) A) diverges B) converges 8-1
A:
Q: 8. Determine if 2n-1 [5 -1 is cont 7n n=1
A: The given series is ∑n=1∞523n-2n-17n. Determine the function is convergent or divergent.
Q: Which test to use and is it convergent/divergent? 1 Σ Z 16n2 – 8n – 3 n=1
A:
Q: 1. da is convergent rod
A: Consider the given integral: ∫1∞1x2dx To test the convergence of integral. Solve the following:…
Q: 1 dx et+ e
A:
Q: Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is…
A: Given that: ∑n=1∞enn!
Q: 9) Determine whether the following integral is divergent or convergent and, if convergent, evaluate…
A:
Q: a) n +h! Convergent BY divergen t t Conve. or dive
A:
Q: Determine if H conver or diverges. Evaluate i it ges converges dx 3
A: We have to find convergence and divergence of integral .Integral is shown as below:
Q: etermine whether the following is convergent or divergent and j
A: Given that,
Q: 10 (f) V4an-1 for n >2 and a1 %3| an
A: To know the function an=4an-1 is convergent or divergent, find the sequence by substituting…
Q: Determine whether E1(-1)" sin n3 is absolute convergent, conditionally convergent, or %=D1…
A: We have to find the series test
Q: If lim=c>0, then both convergent and both divergent. ylgn O Ihi O
A: If limn→∞anbn=c>0, then ∑bn, ∑an both convergent and both divergent. (a) True (b) false
Q: 2. For each of the integrals below if convergent evaluate the integral, otherwise show that it is…
A: Given: the integral below if convergent evaluate the integral, otherwise show that it is divergent.
Q: 9. Let a be a positive value. State the integral test, and use this to determine whether ). -an e…
A:
Q: 1 d.x (г — 1)2
A:
Q: X° +4x dx x* +3x² +2 4 2 1
A: Topic :- Integration If the limit exists as a real number, then the simple improper integral is…
Q: 9. Let a be a positive value. State the integral test, and use this to determine whether > -an e n=0…
A:
Q: +00 (e) Σ (-1)" (n+1) In(n+1) n=100
A: The given problem is to determine whether the given series is convergent or divergent. We can check…
Q: Determine whether the scries is absolutely convergent, conditionally convergent, or divergent. (a) E…
A:
Q: If E, 2"an converges and E o(-1)"2"an diverges, then the radius of conver- gence of o anx" is 2.
A: According to the given information, Suppose,
Q: Applying the limit comparison test, show that the series 1.1 1 2n diverges.
A: The given series is: 12+14+16+...+12n+... The series ca be written as: ∑n=1∞12n
Q: Σ 1. 4n n=1
A:
Q: +00 Inn E(-1)": n2 n=2
A: Solution
Q: Determine if the improper integral is convergent or divergent, and calculate its value if it is…
A: Given, I=∫0∞5e-5xdx
Q: 6. Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. ∫…
A:
Q: dx Show that the integral (p is a positive constant) converges if and only 2x (Inx if p>1. Let a, =,…
A: Given a) ∫2∞dx2x(lnx)p b) an=n2n, if n is a prime number12n, otherwise
Q: SELECT AL A) diverges by divergence test B) diverges C) converges by integral test D) converges by…
A:
Q: dx is convergent a) true b) false O b
A: The given integral is: ∫1∞1x2dx To find it is convergent or divergent. The integral is convergent if…
Q: 7. Determine if f In (x") dx is convergent or divergent. Justify your results.
A: Note:- We are entitles to solve the first question, unless specified. To determine:- ∫0eln(x2) dx is…
Evaluate and see if it is convergent or divergent
Step by step
Solved in 2 steps with 2 images