Explanation Given information: The given series is ln ( 1 + x 1 − x ) = 2 ( x + x 3 3 + x 5 5 + ⋅ ⋅ ⋅ ) . Calculation: Write the given function. f ( x ) = ln ( 1 + x 1 − x ) = ln ( 1 + x ) − ln ( 1 − x ) (1) Refer Table 9.1, “Frequently used Taylor series” in the textbook. Take the Taylor series for the term ln ( 1 + x ) as ( x − x 2 2 + x 3 3 − ⋅ ⋅ ⋅ ) . Replace x in this term as – x to get the Taylor series for the term ln ( 1 − x ) . Substitute ( x − x 2 2 + x 3 3 − ⋅ ⋅ ⋅ ) for ln ( 1 + x ) and ( − x − x 2 2 − x 3 3 − ⋅ ⋅ ⋅ ) for ln ( 1 − x ) in Equation (1)

University Calculus: Early Transcendentals (4th Edition)

4th Edition

ISBN: 9780134995540

Author: Joel R. Hass, Christopher E. Heil, Przemyslaw Bogacki, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

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Chapter 9.10, Problem 53E

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Verify that the given series is correct or wrong for the function ln(1+x1−x).

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Chapter 9.10, Problem 52E

Chapter 9.10, Problem 54E

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Verify that the given series is correct or wrong for the function ln ( 1 + x 1 − x ) .

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Verify that the given series is correct or wrong for the function ln(1+x1−x).

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