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Chapter 7: Q. 25 (page 592)

In Exercises, find a plausible formula for the general term of the given sequence.

0,1,0,1,0,1,鈥�

Short Answer

Expert verified

The plausible formula for the general term of the sequence isak=121+-1k.

Step by step solution

01

Step 1. Given information.

The given sequence is0,1,0,1,0,1,鈥�.

02

Step 2. plausible formula for the general term. 

the sequence 0,1,0,1,0,1,鈥�has 0&1alternately.

the sequence can be written as follows.

role="math" localid="1649186161903" 121+-1kk=1鈭�=0,1,0,1,0,1,鈥�

where for every odd value of k,the term will be zero

For every even value ofk,the term will be one.

So plausible formula for the general term of the sequence is role="math" localid="1649186184028" ak=121+-1k

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Most popular questions from this chapter

Explain why the integral test may be used to analyze the given series and then use the test to determine whether the series converges or diverges.

鈭�k=0鈭�鈥�e鈭�k鈭�k=0鈭�鈥�e鈭�k

What is meant by the remainder Rn of a series 鈭�k=1鈭�ak

Given thata0=-3,a1=5,a2=-4,a3=2and鈭�akk=2鈭�=7, find the value of鈭�akk=4鈭�.

True/False:

Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.

(a) True or False: If ak鈫�0, then 鈭�k=1鈭�akconverges.

(b) True or False: If 鈭�k=1鈭�akconverges, then ak鈫�0.

(c) True or False: The improper integral 鈭�1鈭�f(x)dxconverges if and only if the series 鈭�k=1鈭�f(k)converges.

(d) True or False: The harmonic series converges.

(e) True or False: If p>1, the series 鈭�k=1鈭�k-pconverges.

(f) True or False: If f(x)鈫�0as x鈫�鈭�, then 鈭�k=1鈭�f(k) converges.

(g) True or False: If 鈭�k=1鈭�f(k)converges, then f(x)鈫�0as x鈫�鈭�.

(h) True or False: If 鈭�k=1鈭�ak=Land {Sn}is the sequence of partial sums for the series, then the sequence of remainders {L-Sn}converges to 0.

Determine whether the series 鈭�k=0鈭�2k+25k-1converges or diverges. Give the sum of the convergent series.
See all solutions

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