1.6-1 The number In 2 may be calculated from the series In 2 = 1-+-+ It is known from analysis that this series converges and that the magnitude of the error in any partial sum is less than the magnitude of the first neglected term. Estimate the number of terms that would be required to calculate In 2 to 10 decimal places.
1.6-1 The number In 2 may be calculated from the series In 2 = 1-+-+ It is known from analysis that this series converges and that the magnitude of the error in any partial sum is less than the magnitude of the first neglected term. Estimate the number of terms that would be required to calculate In 2 to 10 decimal places.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 81E
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Transcribed Image Text:1.6-1 The number In
may be calculated from the series
In 2 = 1 -+}-+·..
It is known from analysis that this series converges and that the magnitude of the error in any
partial sum is less than the magnitude of the first neglected term. Estimate the number of
terms that would be required to calculate In 2 to 10 decimal places.
1.6-2 For h near zero it is possible to write
tan h
- 1 + 0(h")
h
tan h
and
- 1 + o(h®)
h
Find the values of y and 8 for which these equalities hold.
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