Theorem 6.5 (page 240 of Apostol) states that if and if then

with

Let and and apply this theorem to approximate with sufficient precision to obtain

By the theorem we have

where

Therefore, letting and we have

Therefore,

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Stumbling Robot

A Fraction of a Dot
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Calculate approximations to * log 2 *

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### Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment):

Theorem 6.5 (page 240 of Apostol) states that if and if then

with

Let and and apply this theorem to approximate with sufficient precision to obtain

By the theorem we have

where

Therefore, letting and we have

Therefore,

The inequality for the lower bound of R_m(x) is incorrect, it should be 2m+1 not 2m-1 both in the denominator and the exponent. Typo probably.