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Chapter 7: Q. 39 (page 592)

Find the least upper bound of the sequences in Exercises 37鈥�42

{-k}

Short Answer

Expert verified

The upper bound is-1.

Step by step solution

01

Step 1. Given information.

The given sequence is{-k}.

02

Step 2. Value of the upper bound.  

The given sequence can be written as,

{-k}={-1,-2,-3,鈥�}

So, the least upper bound of the sequence is-1.

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Most popular questions from this chapter

Given thata0=-3,a1=5,a2=-4,a3=2and鈭�akk=2鈭�=7, find the value ofrole="math" localid="1648828803227" 鈭�akk=3鈭�.

In Exercises 48鈥�51 find all values of p so that the series converges.

鈭�k=2鈭�1klnkp

Provide a more general statement of the integral test in which the function f is continuous and eventually positive, and decreasing. Explain why your statement is valid.

Find the values of x for which the series 鈭�K=0鈭�sinxkconverges.

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.
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