Homework Help is Here – Start Your Trial Now!
Math
Calculus
sin(1/k) Σ 00 k2 k=1

sin(1/k) Σ 00 k2 k=1

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question

Using the Direct Comparison Test or the Limit Comparison Test determine if the series converges or diverges.

**Transcription for Educational Website:** Equation 23: Evaluate the infinite series \[ \sum_{k=1}^{\infty} \frac{\sin(1/k)}{k^2} \] This mathematical expression represents an infinite series where the variable \( k \) starts at 1 and increments by 1 for each term towards infinity. The function inside the series is defined by the ratio of \(\sin(1/k)\) to \(k^2\). - **\(\sin(1/k)\)**: This part of the expression applies the sine function to the reciprocal of \( k \). As \( k \) becomes very large, \( \sin(1/k) \) approaches \(\sin(0)\), which is 0. - **\(k^2\)**: This denotes that each term in the denominator is the square of the current value of \( k \). The series combines these elements and sums them as \( k \) increases towards infinity. This type of series is often analyzed to determine its convergence or divergence.
Transcribed Image Text:**Transcription for Educational Website:** Equation 23: Evaluate the infinite series \[ \sum_{k=1}^{\infty} \frac{\sin(1/k)}{k^2} \] This mathematical expression represents an infinite series where the variable \( k \) starts at 1 and increments by 1 for each term towards infinity. The function inside the series is defined by the ratio of \(\sin(1/k)\) to \(k^2\). - **\(\sin(1/k)\)**: This part of the expression applies the sine function to the reciprocal of \( k \). As \( k \) becomes very large, \( \sin(1/k) \) approaches \(\sin(0)\), which is 0. - **\(k^2\)**: This denotes that each term in the denominator is the square of the current value of \( k \). The series combines these elements and sums them as \( k \) increases towards infinity. This type of series is often analyzed to determine its convergence or divergence.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS