1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lukranit [14]
3 years ago
14

A sequence{an} is given by a1=sqrt(2), an+1=sqrt(2+an).

English
1 answer:
MrMuchimi3 years ago
3 0
It is clear that a(n)=2^(1-2^(-n)). In fact, for n=1 this produces 2^(1-1/2)=sqrt(2)=a1 and if it is true for a(n) then a(n+1) = sqrt (2 * 2^(1-2^(-n))) = sqrt(2^(2-2^(-n))) = 2^(1-2^(-(n+1))) (a) clearly 2^(1-2^(-n))<2<3 so the sequence is bounded by 3. Also a(n+1)/a(n) = 2^(1-2^(-n-1) - 1+2^(-n)) = 2^(1/2^n - 1/2^(n+1)) = 2^(1/2^(n+1)) >1 so the sequence is monotonically increasing. As it is monotonically increasing and has an upper bound it means it has a limin when n-> oo (b) 1-1/2^n -> 1 as n->oo so 2^(1-2^(-n)) -> 2 as n->oo
You might be interested in
Select the correct sentence.
Archy [21]

Answer:

I think it is C I don't see the need for using the punctuation marks

3 0
2 years ago
Watch this video of Endurance collapsing. Crew member Frank Hurley captured this footage. How do the tone and representation of
leonid [27]

Your answer should include some of these points:

The scope of the chapter is completely different from that of the video. The video is of a small segment of the expedition.

The video’s mood is gloomy because it shows the destruction of the ship Endurance. Although the memoir describes the three men facing extreme hardship, the mood is less dismal because the men follow their plan with determination.

The video is shot by crew member Frank Hurley, and the memoir is written by Shackleton. As the expedition’s leader, Shackleton’s level of involvement is much deeper than Hurley's.

The tone of the memoir is personal and the point of view is first person. The video is dramatic and evokes shock in the audience.

The memoir is a realistic but emotional description of the trek and evokes both sympathy and hope in readers. The video is realistic and documentary in style.

4 0
3 years ago
Read 2 more answers
Do you horse ride if so<br> ona scale of 1 to 10 how good are you<br> what sport do you do
posledela
I ride horses on a scale of 1-10 I would give myself a 8 ig
I play basketball, soccer, volleyball, and rodeos
Hope this helps have a nice day!
6 0
3 years ago
Which country was social studies first taught in/4641030/59ceee67?utm_source=registration
Radda [10]
Great Britain but some scholars seem to think United States as well. split view ‍♂️
6 0
3 years ago
Read 2 more answers
Can someone help me with my 8th grade language arts IXL's <br><br> they have to be 100%
Olin [163]

Answer:

Whats the question tho?

Explanation:

8 0
2 years ago
Other questions:
  • Which literary technique does the poet use in these lines from Beowulf?
    5·2 answers
  • Leon stared at the new moccasins that Teofilo had made for the ceremonial dances in the summer. They were nearly hidden by the r
    16·2 answers
  • Which word is a preposition in the following sentence? Yellow is a great color for brightening a room.
    10·1 answer
  • If you were Odysseus, and you were trying to get home after twenty years, which factors would motivate you the most? Check all t
    8·1 answer
  • A _____ is a group of letters that have a particular meaning which appears at the beginning of a word.
    14·2 answers
  • Read the research question.
    6·2 answers
  • A recurring statement in Genesis, Chapter 1, related to language begins with these three words: "And God______ ."
    15·1 answer
  • WILL MARK BRAINLY
    12·1 answer
  • Read this excerpt from "The Tell-Tale Heart" by Edgar Allan Poe.
    7·2 answers
  • 2. As you read George and Hazel's discussion about breaking the laws, what is the best question to ask yourself?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!