Explanation Formula used: Sum of first n terms of the geometric sequence “The sum of first n terms of the geometric sequence with first term a and common ration r is given by, S n = a ( r n − 1 ) r − 1 , where r ≠ 1 ”. Result used: The sum S n = a + a r + a r 2 + ⋯ + a r n − 1 can be written in summation notation as S n = ∑ i = 0 n − 1 a r i . Calculation: The given sum is ∑ i = 0 8 64 ( 1 2 ) i . Compare the given sum with S n = ∑ i = 0 n − 1 a r i . Since the summation is from i = 0 to n − 1 = 8 , the value of n is 9

Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)

11th Edition

ISBN: 9780133886832

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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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 12.1, Problem 37E

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To evaluate: The given sum using the formula for the sum of the first n terms of a geometric sequence.

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Chapter 12.1, Problem 36E

Chapter 12.1, Problem 38E

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Chapter 12 Solutions

Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)

Ch. 12.1 - Find the first four terms of the sequence having...Ch. 12.1 - Prob. 2YT Ch. 12.1 - Prob. 3YT Ch. 12.1 - Prob. 4YT Ch. 12.1 - Prob. 5YT Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - List the first n terms of the geometric sequence...Ch. 12.1 - Prob. 5E

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