From the well known relation...
(1)
... where is the so called 'Euler's constant' we derive...
(2)
... and because is...
(3)
... we have...
(4)
Kind regards
Prove that the sequence (why do they call it a sequence?):
has a limit 'a', which is in the range [ ]
I don't even know how to look at it : as a series, or as a sequence. I know it should be really easy, and should use some plain lemmas or convergence tests, I just don't know which one.
Thanks!
the lower bound is obvious :
since
the series is greater than
if n tends to infinity ,
For the upper bound ,
Consider
we can see that for
is min. when
is max.
therefore ,
could be the upper bound which is better than 1.5