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

If1k2<bkfor every positive integer k, then the series 鈭�k=1鈭�bkdiverges. The objective is to determine whether 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 given statement is true or false by comparison test

02

According to comparison test

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

If the series 鈭�k=1鈭�bkis convergence , then the series 鈭�akk=1鈭�also converges.

we cannot able to determine the convergence and divergence of鈭�k=1鈭�bk

we cannot say about the behavior of the series 鈭�k=1鈭�bkif 1k2<bkholds .

Hence the given statement is false .

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Most popular questions from this chapter

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