Explanation Given information: ∑ x = 1 n x = n ( n + 1 ) 2 for n = 10 , 50 , and 100 . Proof: Use the graphing calculator TI-84 to compute the finite sum of the expression. The command is sum ( seq ( f ( X ) , X , m , n , 1 ) ) , where f ( x ) is an expression involving x , X is the variable used in the expression as the index of summation, m is the starting value, and n is the ending value which should be entered in the calculator to calculate the finite sum of the given series. The steps to find the finite sum usingTI-84 calculator are as follows: For n = 10 : Step 1: Press [ 2 nd ] [ STAT ] to access LIST then go to [ MATH ] and then press 5 , to get s u m ( . Step 2: Again press [ 2 nd ] [ STAT ] to access LIST then go to [ OPS ] and then press 5 , to get s e q ( command then the input is appeared in the window as shown below: Expr : x Variable : X Start : 1 End : 10 Step : 1 Paste Fill these parameters by pressing [ ENTER ] . Step 3: Move the cursor on “Paste” and press [ ENTER ] and complete the right parentheses ) . The output will display on the screen - sum ( seq ( x , X , 1 , 10 , 1 ) ) . Step 4: Press [ ENTER ] and the answer of the output will be displayed as: 55 . Substitute n = 10 in the formula n ( n + 1 ) 2 . 10 ( 10 + 1 ) 2 = 10 ( 11 ) 2 = 55 Hence, ∑ x = 1 10 x = 10 ( 10 + 1 ) 2 . This proves that, ∑ x = 1 n x = n ( n + 1 ) 2 for n = 10 . For n = 50 : Step 1: Press [ 2 nd ] [ STAT ] to access LIST then go to [ MATH ] and then press 5 , to get s u m ( . Step 2: Again press [ 2 nd ] [ STAT ] to access LIST then go to [ OPS ] and then press 5 , to get s e q ( command then the input appears in the window as shown below: Expr : x Variable : X Start : 1 End : 50 Step : 1 Paste Fill these parameters by pressing [ ENTER ]

15th Edition

ISBN: 9780137590896

Author: Larry J. Goldstein; David C. Lay; David I. Schneider; Nakhle H. Asmar; William Edward Tavernetti

Publisher: Pearson Education (US)

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Chapter 11.3, Problem 47E

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To prove: The formula ∑x = 1nx = n( n + 1)2 for n =10, 50, and 100.

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Chapter 11.3, Problem 46E

Chapter 11.3, Problem 48E

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Chapter 11 Solutions

Calculus & Its Applications

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Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - Prob. 15E Ch. 11.1 - Prob. 16E Ch. 11.1 - Prob. 17E Ch. 11.1 - Prob. 18E Ch. 11.1 - Determine the third and fourthTaylor polynomial...Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Graph the function Y1=11x and its fourth Taylor...Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.2 - Prob. 1CYU Ch. 11.2 - Prob. 2CYU Ch. 11.2 - In Exercises 18, use three repetitions of the...Ch. 11.2 - In Exercises 18, use three repetitions of the...Ch. 11.2 - Prob. 3E Ch. 11.2 - Prob. 4E Ch. 11.2 - In Exercises 18, use three repetitions of the...Ch. 11.2 - Prob. 6E Ch. 11.2 - Prob. 7E Ch. 11.2 - Prob. 8E Ch. 11.2 - Sketch the graph of y=x3+2x+2, and use the...Ch. 11.2 - 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To prove: The formula ∑ x = 1 n x = n ( n + 1 ) 2 for n = 10 , 50 , and 100 .

Solution Summary: The author explains how to use the graphing calculator TI-84 to compute the finite sum of the expression.

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To prove: The formula ∑x = 1nx = n( n + 1)2 for n =10, 50, and 100.

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Chapter 11 Solutions