Explanation Given: The given sequence is a n = 24 n 3 [ n ( n + 1 ) ( 2 n + 1 ) 6 ] Here, a n is the n th term of the sequence n is an integer. Calculation: If a n converges to a finite number when n becomes infinitely large than the given sequence is convergent and if it does not converges to any number than it is divergent. Also, if lim n → ∞ a n exists than the sequence is convergent otherwise it is divergent. Rewrite the given sequence and simplify, a n = 24 6 [ n ( n + 1 ) ( 2 n + 1 ) n 3 ] = 4 [ n n ⋅ ( n + 1 n ) ⋅ ( 2 n + 1 n ) ] = 4 [ 1 ⋅ ( 1 + 1 n ⋅ ) ( 2 + 1 n ) ] Simplify, the above equation, a n = 4 [ ( 1 + 1 n ) ⋅ ( 2 + 1 n ) ] From above equation if n approaches infinitely large value than a n approaches a finite number

Bundle: College Algebra, 7th + WebAssign Printed Access Card for Stewart/Redlin/Watson's College Algebra, 7th Edition, Single-Term

7th Edition

ISBN: 9781305618152

Author: Lothar Redlin, Saleem Watson, James Stewart

Publisher: CENGAGE C

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 13.4, Problem 33E

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To Find: The limit of the sequence an=24n3[n(n+1)(2n+1)6] if it is convergent, if it divergent explain why.

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Chapter 13.4, Problem 32E

Chapter 13.4, Problem 34E

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Chapter 13 Solutions

Bundle: College Algebra, 7th + WebAssign Printed Access Card for Stewart/Redlin/Watson's College Algebra, 7th Edition, Single-Term

Ch. 13.1 - When we write limxaf(x)=L then, roughly speaking,...Ch. 13.1 - We write limxaf(x)=L and say that the ______ of...Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

Ch. 13.1 - Prob. 11E Ch. 13.1 - Prob. 12E Ch. 13.1 - Prob. 13E Ch. 13.1 - Estimating Limits Numerically and Graphically Use...Ch. 13.1 - Prob. 15E Ch. 13.1 - Prob. 16E Ch. 13.1 - Prob. 17E Ch. 13.1 - Limits from a Graph For the function f whose graph...Ch. 13.1 - Limits from a Graph For the function f whose graph...Ch. 13.1 - Limits from a Graph For the function f whose graph...Ch. 13.1 - Prob. 21E Ch. 13.1 - Prob. 22E Ch. 13.1 - Prob. 23E Ch. 13.1 - Estimating Limits Graphically Use a graphing...Ch. 13.1 - Prob. 25E Ch. 13.1 - Prob. 26E Ch. 13.1 - Prob. 27E Ch. 13.1 - Prob. 28E Ch. 13.1 - Prob. 29E Ch. 13.1 - One-Sided Limits Graph the piecewise-defined...Ch. 13.1 - Prob. 31E Ch. 13.1 - Prob. 32E Ch. 13.1 - Prob. 33E Ch. 13.1 - DISCUSS: Graphing Calculator Pitfalls (a)...Ch. 13.2 - Suppose the following limits exist:...Ch. 13.2 - If f is a polynomial or a rational function and a...Ch. 13.2 - Limits from a Graph The graphs of f and g are...Ch. 13.2 - Prob. 4E Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Prob. 6E Ch. 13.2 - Prob. 7E Ch. 13.2 - Prob. 8E Ch. 13.2 - Prob. 9E Ch. 13.2 - Prob. 10E Ch. 13.2 - Prob. 11E Ch. 13.2 - Prob. 12E Ch. 13.2 - Prob. 13E Ch. 13.2 - Prob. 14E Ch. 13.2 - Prob. 15E Ch. 13.2 - Prob. 16E Ch. 13.2 - Prob. 17E Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Prob. 19E Ch. 13.2 - Prob. 20E Ch. 13.2 - Prob. 21E Ch. 13.2 - Prob. 22E Ch. 13.2 - Prob. 23E Ch. 13.2 - Prob. 24E Ch. 13.2 - Prob. 25E Ch. 13.2 - Prob. 26E Ch. 13.2 - Prob. 27E Ch. 13.2 - Prob. 28E Ch. 13.2 - Prob. 29E Ch. 13.2 - Prob. 30E Ch. 13.2 - Prob. 31E Ch. 13.2 - Prob. 32E Ch. 13.2 - Prob. 33E Ch. 13.2 - Prob. 34E Ch. 13.2 - Prob. 35E Ch. 13.2 - Prob. 36E Ch. 13.2 - Prob. 37E Ch. 13.2 - Prob. 38E Ch. 13.2 - Prob. 39E Ch. 13.2 - Prob. 40E Ch. 13.2 - Does the Limit Exist? 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The limit of the sequence a n = 24 n 3 [ n ( n + 1 ) ( 2 n + 1 ) 6 ] if it is convergent, if it divergent explain why.

Solution Summary: The author explains that if a_n converges to a finite number when n becomes infinitely large, the sequence is divergent.

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To Find: The limit of the sequence an=24n3[n(n+1)(2n+1)6] if it is convergent, if it divergent explain why.

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Chapter 13 Solutions