Chapter 7: Q. 14 (page 631)

If $\lim_{k 鈫� 鈭�} \frac{a_{k}}{b_{k}} Where L i s$ a positive finite number, what may we conclude about the two series?

Short Answer

Expert verified

$Hence \lim_{k 鈫� 鈭�} \frac{a_{k}}{b_{k}} = L Where L is any positive real number then either both converges or diverges .$

Step by step solution

Step 1. Given information

$\lim_{k 鈫� 鈭�} \frac{a_{k}}{b_{k}} = L$

Step 2. Limit comparison test

$The limit comparison test states that for and be two series with positive terms then If \lim_{k 鈫� 鈭�} \frac{a_{k}}{b_{k}} = L Where L is any positive real number then either both converges or diverges . If \lim_{k 鈫� 鈭�} \frac{a_{k}}{b_{k}} = 0 and {鈭�}_{k = 1}^{鈭�} b_{k} converges then {鈭�}_{k = 1}^{鈭�} a_{k} converges . If \lim_{k 鈫� 鈭�} \frac{a_{k}}{b_{k}} = 鈭� and {鈭�}_{k = 1}^{鈭�} b_{k} diverges then {鈭�}_{k = 1}^{鈭�} a_{k} diverges .$

Step 3. Result

$Hence \lim_{k 鈫� 鈭�} \frac{a_{k}}{b_{k}} = L Where L is any positive real number then either both converges or diverges .$

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91影视

If $\lim_{k 鈫� 鈭�} \frac{a_{k}}{b_{k}} Where L i s$ a positive finite number, what may we conclude about the two series?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Limit comparison test

Step 3. Result

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91影视

If limk鈫�鈭�akbkWhereLis a positive finite number, what may we conclude about the two series?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Limit comparison test

Step 3. Result

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Pure Maths

Mechanics Maths

Logic and Functions

Decision Maths

Study anywhere. Anytime. Across all devices.

If $\lim_{k 鈫� 鈭�} \frac{a_{k}}{b_{k}} Where L i s$ a positive finite number, what may we conclude about the two series?