Question

Evaluating a Sum Find the sum. $$ \sum_{k=1}^{3} \frac{1}{k} $$

   Evaluating a Sum Find the sum.
$$
\sum_{k=1}^{3} \frac{1}{k}
$$

Algebra and Trigonometry

Algebra and Trigonometry

James Stewart,… 4th Edition

Chapter 13, Problem 49

Instant Answer

Solved by Expert Ad F

07/24/2019

Step 1

This means we need to calculate the value of 1/k for each integer k in the range from 1 to 3, and then add these values together. So, we have: $$ \sum_{k=1}^{3} \frac{1}{k} = \frac{1}{1} + \frac{1}{2} + \frac{1}{3} $$ Show more…

Show all steps

lock

Thanks for your feedback!

Evaluating a Sum Find the sum. $$ \sum_{k=1}^{3} \frac{1}{k} $$

Play audio

Feedback

Powered by NumerAI

Ad F and 52 other subject Precalculus educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Finite Series

A finite series is a sum that contains a limited number of terms. The concept is important in various areas of mathematics because it allows for the explicit calculation of sums and serves as a foundational analogue to infinite series, where techniques such as partial sums are used to analyze convergence and estimate values.

Summation Notation

Summation notation is a concise way to represent the addition of a series of terms, typically using the sigma symbol (?) along with an index that specifies the starting and ending values. It is fundamental in mathematics for expressing series and complex sums, simplifying the representation of lengthy addition operations into a compact form.

Harmonic Series

The harmonic series involves the sum of the reciprocals of the natural numbers. When summed over a finite interval, it produces a specific type of series known as a finite harmonic sum or harmonic number. Understanding the harmonic series is pivotal for insights into number theory and analysis, as well as for grasping the behavior of series that grow logarithmically.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later