Question

an+1 for all values of n. What 1. Let {an} be a sequence of positive, real numbers such that is lim an? Explain how you got y

0 0
Add a comment Improve this question Transcribed image text
Answer #1

Goli 0 Lim nyos anth an = dimi n+4 noto 3nth = Lim ngoo n(174/h) nc 3 tyn) = Lim (14/n) = nto 8 <1 (3 +/n) yaa - since the boplz like the answer

Add a comment
Know the answer?
Add Answer to:
an+1 for all values of n. What 1. Let {an} be a sequence of positive, real...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • 18. If ai, az, as,... is a bounded sequence of real numbers, define lim sup an...

    18. If ai, az, as,... is a bounded sequence of real numbers, define lim sup an (also denoted lim an) to be --+ n+ l.u.b. {z ER: an > & for an infinite number of integers n} and define lim inf an (also denoted lim an) to be g.l.b. {ER: An <for an infinite number of integers n}. Prove that lim inf an Slim sup an, with the equality holding if and only if the sequence converges. 19. Let ai,...

  • 1. Let {n} be a sequence of non negative real numbers, and suppose that limnan =...

    1. Let {n} be a sequence of non negative real numbers, and suppose that limnan = 0 and 11 + x2 + ... + In <oo. lim sup - n-00 Prove that the sequence x + x + ... + converges and determine its limit. Hint: Start by trying to determine lim supno Yn. What can you say about lim infn- Yn? 3 ) for all n Expanded Hint: First, show that given any e > 0 we have (...

  • PROVE OR DISPROVE 1. If {an} is a non-increasing sequence of positive real numbers such that...

    PROVE OR DISPROVE 1. If {an} is a non-increasing sequence of positive real numbers such that Σ" an converges, then lim na 0

  • Let (an)nen be a bounded sequence in R. For all n e N define bn =...

    Let (an)nen be a bounded sequence in R. For all n e N define bn = sup{am, On+1, On+2,...}. (You do not have to show that the supremum exists.) (a) Prove that the sequence (bn)nen is a monotone sequence. (b) Prove that the sequence (bn)nen is convergent. (c) Prove or disprove: lim an = lim bre. 100 000

  • 41. Let (an) be a sequence of strictly positive real numbers and Sn = ak (a)...

    41. Let (an) be a sequence of strictly positive real numbers and Sn = ak (a) Suppose that the series Σ an/ S,. an is convergent, determine the nature of the series an is divergent, show that 00 (b) Suppose that the series 1 1 Sn-1 Sp an a/S Then deduce the nature of the series 41. Let (an) be a sequence of strictly positive real numbers and Sn = ak (a) Suppose that the series Σ an/ S,. an...

  • 3.) Let ak E R with ak > 0 for all k E N. Suppose Σ㎞iak...

    3.) Let ak E R with ak > 0 for all k E N. Suppose Σ㎞iak converges. Show that Σί1bk (By definition, for a sequence (ck), we say liCkoo if, for all M ER with Hint: Show that there exists (Ni))ไ1 with N > Nj for all j E N, such that bk there exists a sequence (bk)k of real numbers such that lim converges = oo and M >0, there exists N E N such that ck > M...

  • can you please explain a and b thanks Fourier Analysis See are two finite sequences of...

    can you please explain a and b thanks Fourier Analysis See are two finite sequences of complex numben 7. Suppose (an)- and (bn)1 Let Br= bn denote the partial sums of the series b with the conventicn 1 Bo=0. (a) Prove the summation by parts formula N-1 anbn aNBN- aM BM-1 (an+1-an)B n M n-M (b) Deduce from this formula Dirichlet's test for convergence of a series: if the partial sums of the seriesb are bounded, and fan} is a...

  • Exercise 15: Let (cn) be a sequence of positive numbers. Prove: lim infºn+1 < lim infch/n....

    Exercise 15: Let (cn) be a sequence of positive numbers. Prove: lim infºn+1 < lim infch/n. n700 Cnn +00 What is the corresponding inequality for the lim sup?

  • Let (an) be a sequence such that lim an = 0. Define the sequence (AR) Exercise...

    Let (an) be a sequence such that lim an = 0. Define the sequence (AR) Exercise 21: by A =ļa, and An = zou-a + ax=a + zam for k21. Prove that an converges to some S if and only if Ax converges to S. N=0 k=0 Exercise 22: (Cauchy condensation test) Let (an) be a sequence such that 0 < antı san a) Show n=0 n=1 Hint: Recall the proof of convergence of for p > 1. Ren for...

  • Q4 20 Points Let (a.) 21 be a sequence of real numbers and a ER such...

    Q4 20 Points Let (a.) 21 be a sequence of real numbers and a ER such that .-+ 4. No fles uploaded Q4.1 10 Points State the definition of " a Please select flies a ". Select files Q4.2 5 Points in 2020. Consider the sequence (6.) 1 given by bn = 24 in <2020 and be Using only the definition of convergence of sequences, show b a . Please select file Select file Q4.3 5 Points Let(). be a...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT