Q. 60 In the following exercise, expan... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 60 (page 1174)

In the following exercise, expand the partial sum and find its value
${鈭�}_{n = 1}^{4} \frac{n}{n + 2}$

Short Answer

Expert verified

Hence,

${鈭�}_{n = 1}^{4} \frac{n}{n + 2} = \frac{1}{3} + \frac{2}{4} + \frac{3}{5} + \frac{4}{6} = \frac{21}{10}$

Step by step solution

Step 1. Given information

$\begin{array}{l} Thepartialsumisgivenas \\ {鈭�}_{n = 1}^{4} \frac{n}{n + 2} \\ Wehavetoexpandandfindthevalueofthepartialsum. \end{array}$

Step 2. Expanding the partial sum

$\begin{array}{l} Wesubstitutethevalues 1, 2, 3, 4 inorder \\ 鈬� {鈭�}_{n = 1}^{4} \frac{n}{n + 2} = \frac{1}{1 + 2} + \frac{2}{2 + 2} + \frac{3}{3 + 2} + \frac{4}{4 + 2} \\ = \frac{1}{3} + \frac{2}{4} + \frac{3}{5} + \frac{4}{6} \end{array}$

Step 3. Calculating the sum

Now,

$\begin{array}{l} 鈬� {鈭�}_{n = 1}^{4} \frac{n}{n + 2} = \frac{1}{3} + \frac{2}{4} + \frac{3}{5} + \frac{4}{6} \\ = \frac{1 脳 20 + 2 脳 15 + 3 脳 12 + 4 脳 10}{60} [鈭� L C M of3,4,5,6is60] \\ = \frac{20 + 30 + 36 + 40}{60} \\ = \frac{126}{60} \\ = \frac{21}{10} \end{array}$

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91影视

In the following exercise, expand the partial sum and find its value
${鈭�}_{n = 1}^{4} \frac{n}{n + 2}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Expanding the partial sum

Step 3. Calculating the sum

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In the following exercise, expand the partial sum and find its value 鈭�n=14nn+2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Expanding the partial sum

Step 3. Calculating the sum

One App. One Place for Learning.

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In the following exercise, expand the partial sum and find its value
${鈭�}_{n = 1}^{4} \frac{n}{n + 2}$