Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. basic math
  3. in this exercise, we examine one of the conditions

In this exercise, we examine one of the conditions of the Alternating Series Test. Consider the...

80.2K

Verified Solution

Question

Basic Math

In this exercise, we examine one of the conditions of theAlternating Series Test. Consider the alternating series

1−1+1/2−1/4+1/3−1/9+1/4−1/16+⋯,

where the terms are selected alternately from the sequences{1/n} and {−1/n^2}.

  1. Explain why the nth term of the given series converges to 0 as ngoes to infinity.

  2. Rewrite the given series by grouping terms in the followingmanner:

    (1−1)+(1/2−1/4)+(1/3−1/9)+(1/4−1/16)+⋯.

    Use this regrouping to determine if the series converges ordiverges.

  3. Explain why the condition that the sequence {an}{an}decreases to a limit of 0 is included in the AlternatingSeries Test.

Answer & Explanation Solved by verified expert
4.0 Ratings (417 Votes)
    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Q

1. Jade is renovating his bathroom and as part of the renovations a plumber is required...

Basic Math
Q

1. The Kenton Food company wished to test four different package designs for a new breakfast...

Statistics
Q

Which of the following questions is most relevant to understanding the Calvin cycle?(A) How does...

Biology
Q

Listen Following a scientific method which of the following is the correct order of steps...

Biology
Q

38 A student does the experiment on tracing the path of a ray of light...

Physics
Q

You put $200 into an account that pays simple interest. Once a year the bank...

Basic Math
Q

Graph the function 1 h x x 1 x 7 9 8 7 6 5...

Algebra
Q

What acronym or nemonic is helping you remember which categories of accounts in the accounting...

Accounting
Q

what is the correct way to report qualified unreimbursed partnership expenses

Accounting
Q

Need answers with FORMULAs in Excel Management is reviewing the profitability of...

Accounting
Q

What statement pertaining to a RRIF is correct? a) The earliest age a RRIF...

Finance
Q

For a one year bond of $2,100 at a simple interest rate of 9% per...

Finance