Explanation Given information: 1 m + 1 + m ( m + 1 ) 2 + m 2 ( m + 1 ) 3 + m 3 ( m + 1 ) 4 + . . . Explanation: Compare the series 1 m + 1 + m ( m + 1 ) 2 + m 2 ( m + 1 ) 3 + m 3 ( m + 1 ) 4 + . . . with a + a r + a r 2 + a r 3 + a r 4 + . . . ⇒ a = 1 m + 1 , a r = m ( m + 1 ) 2 ⇒ 1 m + 1 × r = m ( m + 1 ) 2 ⇒ r = m m + 1 Here, | r | = | m m + 1 | = m m + 1 < 1 for any positive integer m . The infinite series a + a r + a r 2 + a r 3 + a r 4 + . . . is convergent if and only if | r | < 1

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ISBN: 9780137590810

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

Publisher: PEARSON

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Chapter 11, Problem 17RE

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The sum of the geometric series 1m+1 + m(m+1)2+ m2(m+1)3+ m3(m+1)4 + . . . if it is convergent. Where, m is a positive integer.

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Chapter 11, Problem 16RE

Chapter 11, Problem 18RE

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The sum of the geometric series 1 m + 1 + m ( m + 1 ) 2 + m 2 ( m + 1 ) 3 + m 3 ( m + 1 ) 4 + . . . if it is convergent. Where, m is a positive integer.

Solution Summary: The author explains that the sum of the geometric series 1m+1 is convergent.

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The sum of the geometric series 1m+1 + m(m+1)2+ m2(m+1)3+ m3(m+1)4 + . . . if it is convergent. Where, m is a positive integer.

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Chapter 11 Solutions