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Math
CalculusMultivariable Calculus8th Edition

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Chapter 11.2, Problem 35E
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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Determine whether the series is convergent or divergent. If it is convergent, find its sum.

35. ∑ k = 1 ∞ ( sin 100 ) k

To determine

Whether the series is convergent or divergent and obtain the sum if the series is convergent.

Explanation

Given:

The series is ∑k=1∞(sin100)k .

Result used:

The geometric series ∑n=1∞arn−1 (or) a+ar+ar2+⋯ is convergent if |r|<1 and its sum is a1−r , where a is the first term and r is the common ratio of the series.

Calculation:

The given series can be written as follows,

∑k=1∞(sin100)k=(sin100)1+(sin100)2+(sin100)3+⋯=(sin100)+(sin100)2+(sin100)3+⋯

Here, the first term of the series is a=sin100 and the common ratio of the series is,

r=(sin100)2sin100=sin100

The absolute value of r is,

|r|=|sin100|=|−0

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Rectangular-to-Cylindrical Conversion In Exercises 9-14, convert the point from rectangular coordinates to cyli...

Calculus: Early Transcendental Functions (MindTap Course List)

CONCEPT CHECK First Derivative Test Describe the First Derivative Test in your own words.

Calculus of a Single Variable

11. For each in the group, define a mapping by for all in. a. Prove that each is a permutation on the set ...

Elements Of Modern Algebra

Problems 17 through 22 refer to Figure 19. (Remember: The sum of the three angles in any triangle is always 180...

Trigonometry (MindTap Course List)

True or False If the series converges to a number s, then all rearrangements of also converge to s.

Study Guide for Stewart's Multivariable Calculus, 8th

What is the partial fraction form of ?

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

In Exercises 16, find the point of intersection of each pair of straight lines. 2x+4y=115x+3y=5

Finite Mathematics for the Managerial, Life, and Social Sciences

In Exercises 17 and 18, complete each proof by filling in the missing statements and reasons. Given: lm34 Prove...

Elementary Geometry for College Students

VolumeIn Exercises 3134, use spherical coordinates to find the volume of the solid. The solid between the spher...

Calculus (MindTap Course List)

Sketching a Polar Graph In Exercises 81-92, sketch a graph of the polar equation. r2=4sin

Calculus

In Exercises 1928, find the conservative vector field for the potential function by finding its gradient. g(x,y...

Multivariable Calculus

The following passage is from the paper Gender Differences in Food Selections of Students at a Historically Bla...

Introduction To Statistics And Data Analysis

Explain how a correlation describes the direction, form, and strength of a relationship and identify these char...

Research Methods for the Behavioral Sciences (MindTap Course List)

Refer to the data in exercise 31. a. Develop an estimated regression equation that can be used to predict Delay...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Divide the following expressions as indicated. (15a2+25a5)(a)

Mathematics For Machine Technology

Explain what is meant by the concept that main effects and interactions are independent.

Research Methods for the Behavioral Sciences (MindTap Course List)

Playbill is a magazine distributed around the country to people attending musicals and other theatrical product...

Statistics for Business & Economics, Revised (MindTap Course List)

Describe the steps you would use to solve a system of a linear equations using Gaussian elimination.

College Algebra (MindTap Course List)

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