Suggested languages for you:

Americas

Europe

Q62.

Expert-verified
Found in: Page 851

### Precalculus Mathematics for Calculus

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

See the step by step solution

## 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 $\sqrt{\frac{0}{2}}+\sqrt{\frac{1}{3}}+\sqrt{\frac{2}{4}}+\sqrt{\frac{4}{5}}.$