ple 5.11.4. If 1 =1+ 1 log n In 1 1 Yn =1+ 2 1 + .+ log n, then prove that {xn} is monotone decreasing and {yn} is monotone increasing and that each converges to the same limit y (Euler's Constant), where 0.3 < < 1.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Example 5.11.4. If
1
1 +
2
1
log n
In
•.. +
%3D
3
1
1
Yn =1+
2
+... +
n
log n,
|
then prove that {xn} is monotone decreasing and {Yn} is monotone increasing and that
each converges to the same limit y (Euler's Constant), where 0.3 < y< 1.
Transcribed Image Text:Example 5.11.4. If 1 1 + 2 1 log n In •.. + %3D 3 1 1 Yn =1+ 2 +... + n log n, | then prove that {xn} is monotone decreasing and {Yn} is monotone increasing and that each converges to the same limit y (Euler's Constant), where 0.3 < y< 1.
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