Chapter 4: Q. 27 (page 325)

Write each of the sums in Exercises 27 in sigma notation. Identify $m$ , $n$ , and $a_{k}$ in each problem.
$\frac{1}{n} + \frac{2}{n} + \frac{3}{n} + \dots + \frac{n}{n}$

Short Answer

Expert verified

Here, $m = 1, n = n$ and $a_{k} = \frac{k}{n}$

\sum_{k = 1}^{n} \frac{k}{n}

Step by step solution

Given information

The given series is $\frac{1}{n} + \frac{2}{n} + \frac{3}{n} + \dots + \frac{n}{n}$ .

Write the series in term of summation

Rewrite the given series in term of summation.

\begin{array}{rcl} \frac{1}{n} + \frac{2}{n} + \frac{3}{n} + \dots + \frac{n}{n} & = & \frac{1 + 2 + 3 + . . . . . + n}{n} \\ = & \frac{\sum_{k = 1}^{n} k}{n} \\ = & \sum_{k = 1}^{n} \frac{k}{n} \end{array}

Write the conclusion

The summation is $\sum_{k = 1}^{n} \frac{k}{n}$ .

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Write each of the sums in Exercises 27 in sigma notation. Identify $m$ , $n$ , and $a_{k}$ in each problem.
$\frac{1}{n} + \frac{2}{n} + \frac{3}{n} + \dots + \frac{n}{n}$

Short Answer

Step by step solution

Given information

Write the series in term of summation

Write the conclusion

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Write each of the sums in Exercises 27 in sigma notation. Identify m, n, and akin each problem.1n+2n+3n+⋯+nn

Short Answer

Step by step solution

Given information

Write the series in term of summation

Write the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Applied Mathematics

Logic and Functions

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

Write each of the sums in Exercises 27 in sigma notation. Identify $m$ , $n$ , and $a_{k}$ in each problem.
$\frac{1}{n} + \frac{2}{n} + \frac{3}{n} + \dots + \frac{n}{n}$