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Chapter 7: Q.1 c) (page 630)

if 0鈮�ak鈮�1kfor every positive integer k, then the series 鈭�k=1鈭�akconverges. The objective is to whether determine the statement is true or false

Short Answer

Expert verified

false

Step by step solution

01

To determine whether given statement is true or false 

To determine whether the given statement is true or not by using comparison test

02

According to comparison test

鈭�k=1鈭�akand 鈭�k=1鈭�bkare two series with positive terms such that 0鈮�ak鈮�bkfor every positive integer k

If 鈭�k=1鈭�bkconverges then the series 鈭�k=1鈭�akalso converges

If the series 鈭�k=1鈭�bk=鈭�k=1鈭�1kis divergent by the power series, So 鈭�k=1鈭�akalso divergence

Hence the given statement is wrong.

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Most popular questions from this chapter

For each series in Exercises 44鈥�47, do each of the following:

(a) Use the integral test to show that the series converges.

(b) Use the 10th term in the sequence of partial sums to approximate the sum of the series.

(c) Use Theorem 7.31 to find a bound on the tenth remainder, R10.

(d) Use your answers from parts (b) and (c) to find an interval containing the sum of the series.

(e) Find the smallest value of n so that localid="1649224052075" Rn鈮�10-6.

鈭�k=0鈭�e-k

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=1鈭�鈥�1+kk2

Express each of the repeating decimals in Exercises 71鈥�78 as a geometric series and as the quotient of two integers reduced to lowest terms.

0.237237237...

What is the contrapositive of the implication 鈥淚f A, then B"?

Find the contrapositives of the following implications:

If a divides b and b dividesc, then a divides c.

Find the values of x for which the series鈭�k=0鈭�xkconverges.
See all solutions

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