Any real number in the interval [0, 1] can be represented by a decimal (not necessarily unique)

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Any real number in the interval [0, 1] can be represented by a decimal (not necessarily unique) as

where d_i is one of the integers 0, 1, 2, 3, . . . , 9. Prove that the series on the right-hand side always converges.

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Thomas Calculus Early Transcendentals

ISBN: 9780321884077

13th Edition

Authors: Joel R Hass, Christopher E Heil, Maurice D Weir

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Question Posted: May 02, 2023 09:27 AM

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Any real number in the interval [0, 1] can be represented by a decimal (not necessarily unique)

Question:

0.djd₂d3d4... || d₁ d₂ + 10 10² + dz d₁ + 10³ 104 +

Step by Step Answer:

ANSWER To prove that the series always converges we can use the comparison test We will compare the ...View the full answer

Thomas Calculus Early Transcendentals

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