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Q62.

Expert-verifiedFound in: Page 851

Book edition
7th Edition

Author(s)
James Stewart, Lothar Redlin, Saleem Watson

Pages
948 pages

ISBN
9781337067508

**Sigma Notation Write the sum without using sigma notation.**

**$\sum _{j=1}^{4}\sqrt{\frac{j-1}{j+1}}$**

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

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

We have to write the sum without using sigma notation.

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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