Explanation Given: S n = 1 4 + 1 12 + 1 24 + ⋯ + 1 2 n ( n + 1 ) S n = 1 4 + 1 12 + 1 24 + ⋯ + 1 2 n ( n + 1 ) The above sum can be written in a general from S n = ∑ n = 1 n 1 2 n ( n + 1 ) This can be simplified as S n = 1 2 ∑ n = 1 n ( 2 n + 2 − 2 n ) 2 n ( n + 1 ) S n = 1 2 ∑ n = 1 n 2 ( n + 1 ) − 2 n 2 n ( n + 1 ) S n = 1 2 ∑ n = 1 n ( 1 n − 1 n + 1 ) By putting the values of n in the above equation S n = 1 2 ( ( 1 − 1 2 ) + ( 1 2 − 1 3 ) + ( 1 3 − 1 4 ) … ( 1

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ISBN: 9780136970866

Author: Blitzer

Publisher: PEARSON

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Chapter 8.4, Problem 43E

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Find $S1$ through $S5$ and use the pattern to make a conjecture about $Sn$ . Prove the conjectural formula of $Sn$ by mathematical induction.

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Chapter 8.4, Problem 42E

Chapter 8.4, Problem 44E

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Kate, Luke, Mary and Nancy are sharing a cake. The cake had previously been divided into four slices (s1, s2, s3 and s4). The following table shows the values of the slices in the eyes of each player. What is fair share to nancy? S1 S2 S3 S4 Kate $4.00 $6.00 $6.00 $4.00 Luke $5.30 $5.00 $5.25 $5.45 Mary $4.25 $4.50 $3.50 $3.75 Nancy $6.00 $4.00 $4.00 $6.00

Kate, Luke, Mary and Nancy are sharing a cake. The cake had previously been divided into four slices (s1, s2, s3 and s4). The following table shows the values of the slices in the eyes of each player. S1 S2 S3 S4 Kate $4.00 $6.00 $6.00 $4.00 Luke $5.30 $5.00 $5.25 $5.45 Mary $4.25 $4.50 $3.50 $3.75 Nancy $6.00 $4.00 $4.00 $6.00 how much is the cak worth to mary

Kate, Luke, Mary and Nancy are sharing a cake. The cake had previously been divided into four slices (s1, s2, s3 and s4). The following table shows the values of the slices in the eyes of each player. What is the threshold of fair share for Luke? S1 S2 S3 S4 Kate $4.00 $6.00 $6.00 $4.00 Luke $5.30 $5.00 $5.25 $5.45 Mary $4.25 $4.50 $3.50 $3.75 Nancy $6.00 $4.00 $4.00 $6.00

Chapter 8 Solutions

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Ch. 8.1 - {an} = a1, a2, a3, a4, , an, represents an...Ch. 8.1 - The nth term of a sequence, represented by an, is...Ch. 8.1 - an = 5n 6 ___Ch. 8.1 - an=(1)n4n1 ____Ch. 8.1 - Prob. 5CVC Ch. 8.1 - 5!, called 5 _______, is the product of all...Ch. 8.1 - (n+3)!(n+2)!= ____Ch. 8.1 - i=1nai=++++. In this summation notation, i is...Ch. 8.1 - In Exercises 1-12, write the first four terms of...Ch. 8.1 - In Exercises 1-12, write the first four terms of...

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Find S 1 through S 5 and use the pattern to make a conjecture about S n . Prove the conjectural formula of S n by mathematical induction.

Solution Summary: The author demonstrates the conjectural formula of S_n by mathematical induction.

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Find $S1$ through $S5$ and use the pattern to make a conjecture about $Sn$ . Prove the conjectural formula of $Sn$ by mathematical induction.

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Chapter 8 Solutions