Chapter 12: Q. 60 (page 1174)

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

Short Answer

Expert verified

Hence,

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

Step by step solution

Step 1. Given information

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

Step 2. Expanding the partial sum

$\begin{array}{l} Wesubstitutethevalues 1, 2, 3, 4 inorder \\ \Rightarrow \sum_{n = 1}^{4} \frac{n}{n + 2} = \frac{1}{1 + 2} + \frac{2}{2 + 2} + \frac{3}{3 + 2} + \frac{4}{4 + 2} \\ = \frac{1}{3} + \frac{2}{4} + \frac{3}{5} + \frac{4}{6} \end{array}$

Step 3. Calculating the sum

Now,

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

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

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 ∑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.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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