The limit 1 log n y = lim [1 + n00 n = 0.57721 56649 01532 86060 65120... is called Euler's constant or sometimes the Euler-Mascheroni constant. Show that the following series converges to y : 1 1 1 1 1 + 3 7 8. - 2 5 6 9 15 Vacca (1910) proved this formula and stated that it is simple and has its natural place near to the Gregory-Leibniz series 1 and Mercator's series 1 log 2 = 1- + - |3
The limit 1 log n y = lim [1 + n00 n = 0.57721 56649 01532 86060 65120... is called Euler's constant or sometimes the Euler-Mascheroni constant. Show that the following series converges to y : 1 1 1 1 1 + 3 7 8. - 2 5 6 9 15 Vacca (1910) proved this formula and stated that it is simple and has its natural place near to the Gregory-Leibniz series 1 and Mercator's series 1 log 2 = 1- + - |3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The limit
1
y = lim [1 +
log n
n
= 0.57721 56649 01532 86060 65120...
is called Euler's constant or sometimes the Euler-Mascheroni constant. Show
that the following series converges to y:
1
+ 2
3
1
1
1
1
+3
7
1
1
+
15
-
-
-
-
4
5
6.
8.
9.
Vacca (1910) proved this formula and stated that it is simple and has its natural
place near to the Gregory-Leibniz series
1
1
4
3
5
7
and Mercator's series
1
log 2 = 1 - ÷ +
1
4
- |3
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