15) 2 +6 + 8 + 10 + ...

Calculus: Early Transcendentals
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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...
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Determine wheter the infinite geometric series coverges or diverges. If it covereges, find its sum

15) 2 +6 + 8 + 10 + ...
Transcribed Image Text:15) 2 +6 + 8 + 10 + ...
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Step 1

Infinite geometric series:

Condition 1:

An infinite geometric series converges if and only if ''the value of common ratio is less than 1'' ( r <1). In this case, sum of the series is equal to a1/(1-r) where a1 is the first term and r is the common ratio.

Condition 2: 

An infinite geometric series diverges if the value of common ratio is more than 1 ( r >1). In this case, sum of the series 

has no limit and the sum approaches infinity.

 

Infinite arithmetic series:

The sum of an infinite arithmetic series is either +∞, if d=positive, or - ∞, if d=negative where d is common difference.

Because the sum of infinite arithmetic series approaches infinity, therefore the infinite arithmetic series diverges.

 

Any other series: 

If the sum of any series approaches infinity then the series diverges.

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