Explanation Given: S = ∑ k = 1 ∞ k − 3 Auxiliary series is R = ∑ n = 1 ∞ ( n ( n + 1 ) ( n + 2 ) ) − 1 Calculation: Step 1: We compute the difference between the general term of the given series and the general term of the auxiliary series: 1 k 3 − 1 k ( k + 1 ) ( k + 2 ) = ( k + 1 ) ( k + 2 ) − k 2 k 3 ( k + 1 ) ( k + 2 ) = 3 k + 2 k 3 ( k + 1 ) ( k + 2 ) Hence, ∑ k = 1 ∞ 1 k 3 = ∑ k = 1 ∞

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Chapter 11.3, Problem 92E

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The value of the series $\sum_{k = 1}^{\infty} k^{- 3}$ to 100 million digit

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Chapter 11.3, Problem 91E

Chapter 11.4, Problem 1PQ

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Chapter 11 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

Ch. 11.1 - Prob. 1PQ Ch. 11.1 - Prob. 2PQ Ch. 11.1 - Prob. 3PQ Ch. 11.1 - Prob. 4PQ Ch. 11.1 - Prob. 5PQ Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E

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The value of the series ∑ k = 1 ∞ k − 3 to 100 million digit

Solution Summary: The author calculates the difference between the general term of the given series and the auxiliary series using a computer algebra system.

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The value of the series $\sum_{k = 1}^{\infty} k^{- 3}$ to 100 million digit

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Chapter 11 Solutions

The value of the series ∑ k = 1 ∞ k − 3 to 100 million digit

Solution Summary: The author calculates the difference between the general term of the given series and the auxiliary series using a computer algebra system.

Videos

The value of the series ∑k=1∞k−3 to 100 million digit

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Chapter 11 Solutions

The value of the series $\sum_{k = 1}^{\infty} k^{- 3}$ to 100 million digit