Chapter 7: Q. 16 (page 652)

Fill in the blanks: Let ${鈭�}_{k = 1}^{鈭�} a_{k}$ and ${鈭�}_{k = 1}^{鈭�} b_{k}$ be two series such that $0 鈮�$ ___ $鈮�$ _ for every . If the series _ converges absolutely, then the series converges absolutely.

Short Answer

Expert verified

On completing the fill in the blanks, we get, "Let ${鈭�}_{k = 1}^{鈭�} a_{k}$ and ${鈭�}_{k = 1}^{鈭�} b_{k}$ be two series such that $0 鈮� a_{k} 鈮� b_{k}$ for every $k > 0$ . If the series ${鈭�}_{k = 1}^{鈭�} b_{k}$ converges absolutely, then the series ${鈭�}_{k = 1}^{鈭�} a_{k}$ converges absolutely.

Step by step solution

Step 1. Given ifnromation.

Consider the given question,

${鈭�}_{k = 1}^{鈭�} a_{k}, {鈭�}_{k = 1}^{鈭�} b_{k}$ are the two series.

Step 2. Fill up the blanks.

Let ${鈭�}_{k = 1}^{鈭�} a_{k}, {鈭�}_{k = 1}^{鈭�} b_{k}$ be the two series such that $0 鈮� a_{k} 鈮� b_{k}$ for every $k > 0$ .

If the series ${鈭�}_{k = 1}^{鈭�} b_{k}$ converges absolutely, then the series ${鈭�}_{k = 1}^{鈭�} a_{k}$ converges absolutely.

Therefore, the first blank is completed by $a_{k}$ , second blank by $b_{k}$ , third blank by $k > 0$ , fourth blank by ${鈭�}_{k = 1}^{鈭�} b_{k}$ and fifth by ${鈭�}_{k = 1}^{鈭�} a_{k}$ .

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91影视

Fill in the blanks: Let ${鈭�}_{k = 1}^{鈭�} a_{k}$ and ${鈭�}_{k = 1}^{鈭�} b_{k}$ be two series such that $0 鈮�$ ___ $鈮�$ _ for every . If the series _ converges absolutely, then the series converges absolutely.

Short Answer

Step by step solution

Step 1. Given ifnromation.

Step 2. Fill up the blanks.

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91影视

Fill in the blanks: Let 鈭�k=1鈭�akand 鈭�k=1鈭�bkbe two series such that 0鈮�_____鈮�_____ for every ______. If the series _____ converges absolutely, then the series converges absolutely.

Short Answer

Step by step solution

Step 1. Given ifnromation.

Step 2. Fill up the blanks.

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

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Study anywhere. Anytime. Across all devices.

Fill in the blanks: Let ${鈭�}_{k = 1}^{鈭�} a_{k}$ and ${鈭�}_{k = 1}^{鈭�} b_{k}$ be two series such that $0 鈮�$ ___ $鈮�$ _ for every . If the series _ converges absolutely, then the series converges absolutely.