Short Answer

Sigma Notation Write the sum without using sigma notation.
$\sum_{j = 1}^{4} \sqrt{\frac{j - 1}{j + 1}}$

The sum is $\sqrt{\frac{0}{2}} + \sqrt{\frac{1}{3}} + \sqrt{\frac{2}{4}} + \sqrt{\frac{4}{5}} .$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given

The given sequence is $\sum_{j = 1}^{4} \sqrt{\frac{j - 1}{j + 1}} .$

Step 2. To determine

We have to write the sum without using sigma notation.

Step 3. Calculation

We’ll plug the values for j, to get rid of the sigma notation.

$\begin{array}{l} \sum_{j = 1}^{4} \sqrt{\frac{j - 1}{j + 1}} \\ = \sqrt{\frac{1 - 1}{1 + 1}} + \sqrt{\frac{2 - 1}{2 + 1}} + \sqrt{\frac{3 - 1}{3 + 1}} + \sqrt{\frac{4 - 1}{4 + 1}} \\ = \sqrt{\frac{0}{2}} + \sqrt{\frac{1}{3}} + \sqrt{\frac{2}{4}} + \sqrt{\frac{4}{5}} \end{array}$

Hence the sum is $\sqrt{\frac{0}{2}} + \sqrt{\frac{1}{3}} + \sqrt{\frac{2}{4}} + \sqrt{\frac{4}{5}} .$

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Precalculus Mathematics for Calculus

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Short Answer

Sigma Notation Write the sum without using sigma notation.
$\sum_{j = 1}^{4} \sqrt{\frac{j - 1}{j + 1}}$

Step by Step Solution

Step 1. Given

Step 2. To determine

Step 3. Calculation

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Sigma Notation Write the sum without using sigma notation.
$\sum_{j = 1}^{4} \sqrt{\frac{j - 1}{j + 1}}$