Hi,
I am trying to calculate:
using the definition only, that is, that , where . If we take take we obtain:
.
I am stuck at this point. Is there any kind of identity, perhaps trigonometric or power series related, to help me evaluate this limit by hand only?
Thank in advanced or any help,
James
Hint:
Use Euler's formula - Wikipedia, the free encyclopedia.
Edit:
An alternative:
Now multiply both sides by .
And third alternative:
Proving by induction:
May be that that is not deriving 'from the first principles' but a possibility is to use the 'geometric sum'...
(1)
Using the 'identity'...
(2)
... and (1) You arrive to write...
(3)
The effective computation of (3) is however 'just a little hard' for me and is left to 'a young mind' ...
Kind regards