Let S = decimal places.) 10000100 x 1. Note that In(n+1) 5 S S 1 + In(n). Note that the sequence (a) = (S-In(n)) is bounded and decreasing. Note that the sequence (a) converges to a limit y (called Euler's constant). Approximate y using a 100 (Round your answer to fo D

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 72E
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n
Let Sn
decimal places.)
0.0100
a 100
1 +
1
X
+
1
n
Note that In(n + 1) ≤ Sµ ≤ 1 + In(n). Note that the sequence {a} = {S₁ - In(n)} is bounded and decreasing. Note that the sequence {a} converges to a limit y (called Euler's constant). Approximate y using a 100. (Round your answer to four
Transcribed Image Text:n Let Sn decimal places.) 0.0100 a 100 1 + 1 X + 1 n Note that In(n + 1) ≤ Sµ ≤ 1 + In(n). Note that the sequence {a} = {S₁ - In(n)} is bounded and decreasing. Note that the sequence {a} converges to a limit y (called Euler's constant). Approximate y using a 100. (Round your answer to four
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